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Actions of large finite groups on manifolds Int. J. Math. (IF 0.6) Pub Date : 2024-04-20 Ignasi Mundet i Riera
In this paper, we survey some recent results on actions of finite groups on topological manifolds. Given an action of a finite group G on a manifold X, these results provide information on the restriction of the action to a subgroup of G of index bounded above by a number depending only on X. Some of these results refer to the algebraic structure of the group, such as being abelian or nilpotent or
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The companion section for classical groups Int. J. Math. (IF 0.6) Pub Date : 2024-04-17 Thomas Hameister, Bao Châu Ngô
We use the companion matrix construction for GLn to build canonical sections of the Chevalley map [𝔤/G]→𝔤//G for classical groups G as well as the group G2. To do so, we construct canonical tensors on the associated spectral covers. As an application, we make explicit lattice descriptions of affine Springer fibers and Hitchin fibers for classical groups and G2.
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Multiplicity algebras for rank 2 bundles on curves of small genus Int. J. Math. (IF 0.6) Pub Date : 2024-04-17 Nigel Hitchin
In [11], Hausel introduced a commutative algebra — the multiplicity algebra — associated to a fixed point of the C∗-action on the Higgs bundle moduli space. Here we describe this algebra for a fixed point consisting of a very stable rank 2 vector bundle and zero Higgs field for a curve of low genus. Geometrically, the relations in the algebra are described by a family of quadrics and we focus on the
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A blowing-up formula for the intersection cohomology of the moduli of rank 2 Higgs bundles over a curve with trivial determinant Int. J. Math. (IF 0.6) Pub Date : 2024-04-17 Sang-Bum Yoo
We prove that a blowing-up formula for the intersection cohomology of the moduli space of rank 2 Higgs bundles over a curve with trivial determinant holds. As an application, we derive the Poincaré polynomial of the intersection cohomology of the moduli space under a technical assumption.
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Equivariant localization in the theory of Z-stability for Kähler manifolds Int. J. Math. (IF 0.6) Pub Date : 2024-04-17 Alexia Corradini
We apply equivariant localization to the theory of Z-stability and Z-critical metrics on a Kähler manifold (X,α), where α is a Kähler class. We show that the invariants used to determine Z-stability of the manifold, which are integrals over test configurations, can be written as a product of equivariant classes, hence equivariant localization can be applied. We also study the existence of Z-critical
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New examples of twisted Brill–Noether loci I Int. J. Math. (IF 0.6) Pub Date : 2024-04-13 L. Brambila-Paz, P. E. Newstead
Our purpose in this paper is to construct new examples of twisted Brill–Noether loci on curves of genus g≥2. Many of these examples have negative expected dimension. We deduce also the existence of a new region in the Brill–Noether map, whose points support non-empty standard Brill–Noether loci.
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Narasimhan–Ramanan branes and wobbly Higgs bundles Int. J. Math. (IF 0.6) Pub Date : 2024-04-13 Emilio Franco, Peter B. Gothen, André Oliveira, Ana Peón-Nieto
Narasimhan–Ramanan branes, introduced by the authors in a previous paper, consist of a family of BBB-branes inside the moduli space of Higgs bundles, and a family of complex Lagrangian subvarieties. It was conjectured that these complex Lagrangian subvarieties support the BBB-branes that are mirror dual to the Narasimhan–Ramanan BBB-branes. In this paper, we show that the support of these branes intersects
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Kähler–Einstein metrics on smooth Fano toroidal symmetric varieties of type AIII Int. J. Math. (IF 0.6) Pub Date : 2024-04-10 Kyusik Hong, DongSeon Hwang, Kyeong-Dong Park
The wonderful compactification Xm of a symmetric homogeneous space of type AIII(2,m) for each m≥4 is Fano, and its blowup Ym along the unique closed orbit is Fano if m≥5 and Calabi–Yau if m=4. Using a combinatorial criterion for K-polystability of smooth Fano spherical varieties obtained by Delcroix, we prove that Xm admits a Kähler–Einstein metric for each m≥4 and Ym admits a Kähler–Einstein metric
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On the monodromy of holomorphic differential systems Int. J. Math. (IF 0.6) Pub Date : 2024-04-05 Indranil Biswas, Sorin Dumitrescu, Lynn Heller, Sebastian Heller, João Pedro dos Santos
First we survey and explain the strategy of some recent results that construct holomorphic sl(2,ℂ)-differential systems over some Riemann surfaces Σg of genus g≥2, satisfying the condition that the image of the associated monodromy homomorphism is (real) Fuchsian [I. Biswas, S. Dumitrescu, L. Heller and S. Heller, Fuchsian sl(2,ℂ)-systems of compact Riemann surfaces [with an appendix by Takuro Mochizuki]
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Higgs bundles twisted by a vector bundle Int. J. Math. (IF 0.6) Pub Date : 2024-04-05 Guillermo Gallego, Oscar García-Prada, M. S. Narasimhan
In this paper, we consider a generalization of the theory of Higgs bundles over a smooth complex projective curve in which the twisting of the Higgs field by the canonical bundle of the curve is replaced by a rank 2 vector bundle. We define a Hitchin map and give a spectral correspondence. We also state a Hitchin–Kobayashi correspondence for a generalization of Hitchin’s equations to this situation
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Simplicity and tracial weights on non-unital reduced crossed products Int. J. Math. (IF 0.6) Pub Date : 2024-04-05 Yuhei Suzuki
We extend theorems of Breuillard–Kalantar–Kennedy–Ozawa on unital reduced crossed products to the non-unital case under mild assumptions. As a result simplicity of C∗-algebras is stable under taking reduced crossed products over discrete C∗-simple groups, and a similar result for uniqueness of tracial weight. Interestingly, our analysis on tracial weights involves von Neumann algebra theory. Our generalizations
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Hermitian mean curvature flow Int. J. Math. (IF 0.6) Pub Date : 2024-04-04 Jieming Yang
A Hermitian curvature flow is proposed and some regularity results are obtained. The stationary solution to the flow, if exists, is a balanced metric which is also Hermitian Yang–Mills with respect to itself.
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Framed parabolic sheaves on a trinion Int. J. Math. (IF 0.6) Pub Date : 2024-04-04 Indranil Biswas, Jacques Hurtubise
We consider for structure groups SU(n)⊂SL(n,ℂ) a densely defined toric structure on the moduli space of framed parabolic sheaves on a three-punctured sphere, which degenerates to an actual toric structure. In combination with previous degeneration results, these extend to similar moduli for arbitrary Riemann surfaces.
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Volume functionals on pseudoconvex hypersurfaces Int. J. Math. (IF 0.6) Pub Date : 2024-04-04 Simon Donaldson, Fabian Lehmann
The focus of this paper is on a volume form defined on a pseudoconvex hypersurface M in a complex Calabi–Yau manifold (that is, a complex n-manifold with a nowhere-vanishing holomorphic n-form). We begin by defining this volume form and observing that it can be viewed as a generalization of the affine-invariant volume form on a convex hypersurface in Rn. We compute the first variation, which leads
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Hitchin map on even very stable upward flows Int. J. Math. (IF 0.6) Pub Date : 2024-04-04 Miguel González, Tamás Hausel
We define even very stable Higgs bundles and study the Hitchin map restricted to their upward flows. In the GLn case, we classify the type (1,…,1) examples, and find that they are governed by a root system formed by the roots of even height. We discuss how the spectrum of equivariant cohomology of real and quaternionic Grassmannians, 4n-spheres and the real Cayley plane appear to describe the Hitchin
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On codimension one holomorphic distributions on compact toric orbifolds Int. J. Math. (IF 0.6) Pub Date : 2024-04-03 Arnulfo Miguel Rodríguez Peña
The number of singularities, counted with multiplicity, of a generic codimension one holomorphic distribution on a compact toric orbifold is determined. As a consequence, we provide a classification for regular distributions on rational normal scrolls and weighted projective spaces. Additionally, under specific conditions, we prove that the singular set of a codimension one holomorphic foliation on
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Quantization of locally compact groups associated with essentially bijective 1-cocycles Int. J. Math. (IF 0.6) Pub Date : 2024-04-03 Pierre Bieliavsky, Victor Gayral, Sergey Neshveyev, Lars Tuset
Given an extension 0→V→G→Q→1 of locally compact groups, with V abelian, and a compatible essentially bijective 1-cocycle η:Q→V̂, we define a dual unitary 2-cocycle on G and show that the associated deformation of Ĝ is a cocycle bicrossed product defined by a matched pair of subgroups of Q⋉V̂. We also discuss an interpretation of our construction from the point of view of Kac cohomology for matched
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Endpoint estimates of variation and oscillation operators associated with Zλ functions Int. J. Math. (IF 0.6) Pub Date : 2024-03-28 Yongming Wen, Yanyan Han, Xianming Hou
This paper obtains weak-type estimates, limiting weak-type behaviors for variation operators associated with Zλ functions. Besides, we give a new characterization of Hardy space via the boundedness of variation operators associated with Zλ functions.
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Twistor space for local systems on an open curve Int. J. Math. (IF 0.6) Pub Date : 2024-03-27 Carlos T. Simpson
Let X=X¯−D be a smooth quasi-projective curve. We previously constructed a Deligne–Hitchin moduli space with Hecke gauge groupoid for connections of rank 2. We extend this construction to the case of any rank r, although still keeping a genericity hypothesis. The formal neighborhood of a preferred section corresponding to a tame harmonic bundle is governed by a mixed twistor structure.
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A non-integrated defect relation for general divisors incorporating the beta constants Int. J. Math. (IF 0.6) Pub Date : 2024-03-25 Chin Jui Yang
In this paper, we incorporate the beta constants into the defect relation and deduce a non-integrated defect relation for meromorphic maps from a Kähler manifold whose universal covering is a ball into a projective variety intersecting general divisors properly.
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Implosion, contraction and Moore–Tachikawa Int. J. Math. (IF 0.6) Pub Date : 2024-03-20 Andrew Dancer, Frances Kirwan, Johan Martens
We give a survey of the implosion construction, extending some of its aspects relating to hypertoric geometry from type A to a general reductive group, and interpret it in the context of the Moore–Tachikawa category. We use these ideas to discuss how the contraction construction in symplectic geometry can be generalized to the hyperkähler or complex symplectic situation.
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Lebesgue points of functions in the complex Sobolev space Int. J. Math. (IF 0.6) Pub Date : 2024-03-13 Gabriel Vigny, Duc-Viet Vu
Let φ be a function in the complex Sobolev space W∗(U), where U is an open subset in ℂk. We show that the complement of the set of Lebesgue points of φ is pluripolar. The key ingredient in our approach is to show that |φ|α for α∈[1,2) is locally bounded from above by a plurisubharmonic function.
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Stability and localization of the Lp Bergman kernel Int. J. Math. (IF 0.6) Pub Date : 2024-03-11 Liyou Zhang, Ziyi Zhang
The aims of this paper are twofold. First, we generalize the classical Ramadanov theorem and Skwarczyński theorem for the L2 Bergman kernels to the Lp case, which are concerned with the compact convergence of Lp Bergman kernels on an increasing or decreasing sequence of domains in ℂn. Second, we prove a localization principle for the Lp Bergman kernel on bounded strongly pseudoconvex domains with smooth
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Normalized quandle twisted Alexander invariants Int. J. Math. (IF 0.6) Pub Date : 2024-03-06 Atsushi Ishii, Kanako Oshiro
We introduce a quandle version of the normalized (twisted) Alexander polynomial, which is an invariant of a pair of an oriented link and a quandle representation. The invariant can be constructed by fixing each Alexander pair, and we find various invariants in our framework, which include the quandle cocycle invariant and the normalized (twisted) Alexander polynomial of a knot. In this paper, we develop
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Locally conformally product structures Int. J. Math. (IF 0.6) Pub Date : 2024-03-05 Brice Flamencourt
A locally conformally product (LCP) structure on compact manifold M is a conformal structure c together with a closed, non-exact and non-flat Weyl connection D with reducible holonomy. Equivalently, an LCP structure on M is defined by a reducible, non-flat, incomplete Riemannian metric hD on the universal cover M̃ of M, with respect to which the fundamental group π1(M) acts by similarities. It was
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A characterization of quasipositive two-bridge knots Int. J. Math. (IF 0.6) Pub Date : 2024-03-02 Burak Ozbagci, Stepan Orevkov
We prove a simple necessary and sufficient condition for a two-bridge knot K(p,q) to be quasipositive, based on the continued fraction expansion of p/q. As an application, coupled with some classification results in contact and symplectic topology, we give a new proof of the fact that smoothly slice two-bridge knots are non-quasipositive. Another proof of this fact using methods within the scope of
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Finsler metrizabilities and geodesic invariance Int. J. Math. (IF 0.6) Pub Date : 2024-02-28 Ioan Bucataru, Oana Constantinescu
We demonstrate that various metrizability problems for Finsler sprays can be reformulated in terms of the geodesic invariance of two tensors, namely the metric and angular tensors. We show that a spray S is the geodesic spray of some Finsler metric if and only if its metric tensor is geodesically invariant. Moreover, we establish that gyroscopic sprays constitute the largest class of sprays characterized
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Some curvature properties of spherically symmetric Finsler metrics Int. J. Math. (IF 0.6) Pub Date : 2024-02-23 Akbar Tayebi, Faezeh Eslami
In this paper, we study some important Remannian and non-Riemannian curvature properties of spherically symmetric Finsler metrics. Under a condition on the geodesic coefficient, we find the necessary and sufficient conditions under which spherically symmetric metrics are of scalar flag curvature, W-quadratic or projectively Ricci-flat. For spherically symmetric metrics of relatively isotropic Landsberg
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The degree 2 part of the LMO invariant of cyclic branched covers of knots obtained by plumbing the doubles of two knots Int. J. Math. (IF 0.6) Pub Date : 2024-02-23 Kouki Yamaguchi
The LMO invariant is a universal quantum invariant of closed oriented 3-manifolds. In this paper, we present the degree 2 part of the LMO invariant of cyclic branched covers of knots by using the 3-loop invariant of knots, and we calculate it concretely for knots obtained by plumbing the doubles of two knots.
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Monotonicity and one-dimensional symmetry of solutions for the weighted fractional parabolic equations on the whole space Int. J. Math. (IF 0.6) Pub Date : 2024-02-20 Ye Li, Chuang Lin, Kelei Zhang
In this paper, we investigate the monotonicity and one-dimensional symmetry of solutions for parabolic equations related to the weighted fractional Laplacian on the whole space. We first establish a generalized weighted average inequality and the maximum principle in unbounded domains, and then carry out the sliding method to obtain monotonicity and one-dimensional symmetry of solutions.
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Force stability of the Boltzmann equations Int. J. Math. (IF 0.6) Pub Date : 2024-02-15 Ming-Jiea Lyu, Kung-Chien Wu
In this paper, we consider the Boltzmann equation with external force in the whole space, where the collision kernel is assumed to be hard potential and cutoff. We prove that the solutions of such Boltzmann equations are Lp (1≤p<∞) stable under the perturbation of external force. Our estimate is based on the gradient estimate of the solution. The key step of this paper is to estimate the solutions
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Distance formulas in Bruhat–Tits building of SLd(ℚp) Int. J. Math. (IF 0.6) Pub Date : 2024-02-14 Dominik Lachman
We study the distance on the Bruhat–Tits building of the group SLd(ℚp) (and its other combinatorial properties). Coding its vertices by certain matrix representatives, we introduce a way how to build formulas with combinatorial meanings. In Theorem 1, we give an explicit formula for the graph distance δ(α,β) of two vertices α and β (without having to specify their common apartment). Our main result
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Equivariant spectral flow and equivariant η-invariants on manifolds with boundary Int. J. Math. (IF 0.6) Pub Date : 2024-02-14 Johnny Lim, Hang Wang
In this paper, we study several closely related invariants associated to Dirac operators on odd-dimensional manifolds with boundary with an action of the compact group H of isometries. In particular, the equality between equivariant winding numbers, equivariant spectral flow and equivariant Maslov indices is established. We also study equivariant η-invariants which play a fundamental role in the equivariant
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Properly outer and strictly outer actions of finite groups on prime C*-algebras Int. J. Math. (IF 0.6) Pub Date : 2024-02-14 Costel Peligrad
An action of a compact, in particular finite group on a C*-algebra is called properly outer if no automorphism of the group that is distinct from identity is implemented by a unitary element of the algebra of local multipliers of the C*-algebra. In this paper, I define the notion of strictly outer action (similar to the definition for von Neumann factors in [S. Vaes, The unitary implementation of a
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Rigidity of self-shrinkers with constant squared norm of the second fundamental form Int. J. Math. (IF 0.6) Pub Date : 2024-02-01 Yu Fu, Dan Yang
In this paper, we investigate the rigidity of self-shrinkers in a Euclidean space ℝn+1. We first prove that any self-shrinker X:M→ℝn+1 with constant squared norm of the second fundamental form and with at most two distinct principal curvatures is an open part of a hyperplane ℝn, a cylinder Sk(k)×ℝn−k (1≤k≤n−1) or the round sphere Sn(n). Then, it can be applied to show that any complete self-shrinker
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On uniqueness of submaximally symmetric parabolic geometries Int. J. Math. (IF 0.6) Pub Date : 2024-01-24 Dennis The
Among the (regular, normal) parabolic geometries of type (G,P), there is a locally unique maximally symmetric structure and it has the symmetry dimension dim(G). The symmetry gap problem concerns the determination of the next realizable (submaximal) symmetry dimension. When G is a complex or split-real simple Lie group of rank at least three or when (G,P)=(G2,P2), we establish a local uniqueness result
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Modular categories of Frobenius–Perron dimension p2q2r2 and perfect modular categories Int. J. Math. (IF 0.6) Pub Date : 2024-01-19 Dewei Zhou, Jingcheng Dong
We prove that modular categories of Frobenius–Perron dimension p2q2r2 are solvable, where p
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Kawaguchi–Silverman conjecture on automorphisms of projective threefolds Int. J. Math. (IF 0.6) Pub Date : 2024-01-12 Sichen Li
Under the framework of dynamics on normal projective varieties by Kawamata, Nakayama and Zhang, and Hu and Li, we may reduce Kawaguchi–Silverman conjecture for automorphisms f on normal projective threefolds X with either the canonical divisor KX is trivial or negative Kodaira dimension to the following two cases: (i) f is a primitively automorphism of a weak Calabi–Yau threefold, (ii) X is a rationally
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Hopf PBW-deformations of a new type quantum group Uq(𝔰𝔩2∗) and deformed preprojective algebras Int. J. Math. (IF 0.6) Pub Date : 2024-01-12 Yongjun Xu, Jialei Chen
We classify all the Hopf PBW-deformations of a new type quantum group Uq(𝔰𝔩2∗) from which the classical Drinfeld–Jimbo quantum group Uq(𝔰𝔩2) can arise as an almost unique nontrivial one. Different from the Uq(𝔰𝔩2) case, the category of finite-dimensional Uq(𝔰𝔩2∗)-modules is non-semisimple. We establish a block decomposition theorem for the category Uq(𝔰𝔩2∗)−mod wt of finite-dimensional weight
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Complex vs. convex Morse functions and geodesic open books Int. J. Math. (IF 0.6) Pub Date : 2024-01-06 Pierre Dehornoy, Burak Ozbagci
Suppose that Σ is a closed and oriented surface equipped with a Riemannian metric. In the literature, there are three seemingly distinct constructions of open books on the unit (co)tangent bundle of Σ, having complex, contact and dynamical flavors, respectively. Each one of these constructions is based on either an admissible divide or an ordered Morse function on Σ. We show that the resulting open
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On bounded coordinates in bimodules Int. J. Math. (IF 0.6) Pub Date : 2023-12-22 Debabrata De, Kunal Mukherjee
We provide a comprehensive study on uniformly left ψ-bounded (respectively, (φ,ψ)-bounded) orthonormal bases in infinite-dimensional cyclic bimodules associated with c.p. maps between two von Neumann algebras M and N, where φ and ψ are faithful normal states on M and N, respectively. Separate investigations on cyclic bimodules associated with Markov maps and arbitrary c.p. maps are also provided since
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Vector invariants of permutation groups in characteristic zero Int. J. Math. (IF 0.6) Pub Date : 2023-12-21 Fabian Reimers, Müfit Sezer
We consider a finite permutation group acting naturally on a vector space V over a field 𝕜. A well-known theorem of Göbel asserts that the corresponding ring of invariants 𝕜[V]G is generated by the invariants of degree at most dimV2. In this paper, we show that if the characteristic of 𝕜 is zero, then the top degree of vector coinvariants 𝕜[Vm]G is also bounded above by dimV2, which implies the
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Geometry of four-dimensional Kähler and para-Kähler Lie groups Int. J. Math. (IF 0.6) Pub Date : 2023-12-08 M. Ferreiro-Subrido, E. García-Río, R. Vázquez-Lorenzo
We classify four-dimensional para-Kähler Lie algebras and study their geometry showing that they are symmetric or simply harmonic special recurrent, in the semi-symmetric case. The non-semi-symmetric case allows essentially two distinct geometries in addition to the 3-symmetric spaces, without a Kählerian counterpart.
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Contact non-squeezing and orderability via the shape invariant Int. J. Math. (IF 0.6) Pub Date : 2023-11-29 Dylan Cant
In this paper, we prove a contact non-squeezing result for a class of embeddings between starshaped domains in the contactization of the symplectization of the unit cotangent bundle of certain manifolds. The class of embeddings includes embeddings which are not isotopic to the identity. This yields a new proof that there is no positive loop of contactomorphisms in the unit cotangent bundles under consideration
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Some characterizations of the complex projective space via Ehrhart polynomials Int. J. Math. (IF 0.6) Pub Date : 2023-11-29 Andrea Loi, Fabio Zuddas
Let PλΣn be the Ehrhart polynomial associated to an integral multiple λ of the standard simplex Σn⊂ℝn. In this paper, we prove that if (M,L) is an n-dimensional polarized toric manifold with associated Delzant polytope Δ and Ehrhart polynomial PΔ such that PΔ=PλΣn, for some λ∈ℤ+, then (M,L)≅(ℂPn,O(λ)) (where O(1) is the hyperplane bundle on ℂPn) in the following three cases: (1) arbitrary n and λ=1
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An anisotropic area-preserving flow and its geometric application Int. J. Math. (IF 0.6) Pub Date : 2023-11-24 Yunlong Yang, Lina Liu
This paper centers its attention on an anisotropic area-preserving flow with the goal of establishing the existence of smooth solutions to the even, planar logarithmic Minkowski problem by the asymptotic behavior of this flow.
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On K-semistable domains — more examples Int. J. Math. (IF 0.6) Pub Date : 2023-11-23 Chuyu Zhou
We compute K-semistable domains for various examples of log pairs.
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Two nonlocal inverse curvature flows of convex closed plane curves Int. J. Math. (IF 0.6) Pub Date : 2023-11-21 Zezhen Sun
In this paper, we introduce two 1/κn-type (n≥1) curvature flows for closed convex planar curves. Along the flows the length of the curve is decreasing while the enclosed area is increasing. Finally, the evolving curves converge smoothly to a finite circle if they do not develop singularity during the evolution process.
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On the Cauchy problem of the two-component Novikov-type system with peaked solutions and H1-conservation law Int. J. Math. (IF 0.6) Pub Date : 2023-08-22 Haiquan Wang, Miaomiao Chen, Gezi Chong
Considered herein is the Cauchy problem for the two-component Novikov-type system with peaked solutions and H1-conservation law. At first, we establish that the solutions maintain corresponding properties at infinity within the lifespan provided that the initial data decay exponentially and algebraically, respectively. Next, the local regularity and analyticity of the solutions to this problem in Sobolev–Gevrey
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Algebraic dependences of meromorphic mappings from complete Kähler manifolds into projective spaces sharing few hyperplanes Int. J. Math. (IF 0.6) Pub Date : 2023-08-17 Duc Thoan Pham
In this paper, we give some results on the algebraic dependence of meromorphic mappings from a complete Kähler manifold whose universal covering is biholomorphic to a ball in ℂm into ℙn(ℂ) sharing few hyperplanes in subgeneral position with truncated multiplicities to level p, where all zeros with multiplicities greater than certain values do not need to be counted. Our results are generalizations
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Surjective morphisms from affine space to its Zariski open subsets Int. J. Math. (IF 0.6) Pub Date : 2023-08-12 Viktor Balch Barth
We prove constructively the existence of surjective morphisms from affine space onto certain open subvarieties of affine space of the same dimension. For any algebraic set Z⊂𝔸n−2⊂𝔸n, we construct an endomorphism of 𝔸n with 𝔸n∖Z as its image. By Noether’s normalization lemma, these results extend to give surjective maps from any n-dimensional affine variety X to 𝔸n∖Z.
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The infinite dihedral group and K3 surfaces with Picard number 2 Int. J. Math. (IF 0.6) Pub Date : 2023-08-11 Kwangwoo Lee
The automorphism group of a K3 surface with Picard number two is either the infinite cyclic group or the infinite dihedral group, if it is infinite. In this paper, we determine some conditions for a K3 surface of Picard number two to have the infinite dihedral automorphism group.
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Invariant means and multipliers on convolution quantum group algebras Int. J. Math. (IF 0.6) Pub Date : 2023-08-07 Ali Ebrahimzadeh Esfahani, Mehdi Nemati, Reza Esmailvandi
Let 𝔾 be a locally compact quantum group. Then the space T(L2(𝔾)) of trace class operators on L2(𝔾) is a Banach algebra with the convolution induced by the right fundamental unitary of 𝔾. We show that properties of 𝔾 such as amenability, triviality and compactness are equivalent to the existence of left or right invariant means on the convolution Banach algebra T(L2(𝔾)). We also investigate the
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The classification of smooth well-formed Fano weighted complete intersections Int. J. Math. (IF 0.6) Pub Date : 2023-07-29 Mikhail Ovcharenko
We show that the set of families of smooth well-formed Fano weighted complete intersections admits a natural partition with respect to the variance var(X)=coind(X)−codim(X). Moreover, we obtain the classification of smooth well-formed Fano weighted complete intersections of small variance. We also prove that the anticanonical linear system on a smooth well-formed Fano weighted complete intersection
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Endpoint regularity of discrete multilinear maximal and minimal operators Int. J. Math. (IF 0.6) Pub Date : 2023-07-29 Jing Li, Feng Liu
We introduce two discrete multilinear maximal and minimal operators associated to the function Φ, which cover the classical discrete multilinear maximal and minimal operators and their fractional variants. Under a more restrictive condition on Φ, we establish some new variation boundedness and continuity of the above operators, which is new and interesting even in the linear case. It should be pointed
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Some results on the comparison principle for the weighted log canonical thresholds Int. J. Math. (IF 0.6) Pub Date : 2023-07-28 Trinh Tung
The purpose of this paper is to establish some results on the comparison principle for the weighted log canonical thresholds of plurisubharmonic functions in case the weight is a measure of the form μ=∥z∥2tdV2n,t≥0 and μ=∥z∥2(k−n)dV2n with 1≤k≤n, where dV2n is the Lebesgue measure in ℂn.
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Poincaré metric of holomorphic foliations with non-degenerate singularities Int. J. Math. (IF 0.6) Pub Date : 2023-07-22 François Bacher
Consider a Brody hyperbolic foliation ℱ with non-degenerate singularities on a compact complex manifold. We show that its leafwise Poincaré metric is transversally Hölder continuous with a logarithmic slope towards the singular set of ℱ.
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Homological dimensions of analytic Ore extensions Int. J. Math. (IF 0.6) Pub Date : 2023-07-21 Petr Kosenko
If A is an algebra with finite right global dimension, then for any automorphism α and α-derivation δ the right global dimension of A[t;α,δ] satisfies rgldA≤rgldA[t;α,δ]≤rgldA+1. We extend this result to the case of holomorphic Ore extensions and smooth crossed products by ℤ of ⊗̂-algebras.
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Turaev–Viro invariants and cabling operations Int. J. Math. (IF 0.6) Pub Date : 2023-07-19 Sanjay Kumar, Joseph M. Melby
In this paper, we study the variation of the Turaev–Viro invariants for 3-manifolds with toroidal boundary under the operation of attaching a (p,q)-cable space. We apply our results to a conjecture of Chen and Yang which relates the asymptotics of the Turaev–Viro invariants to the simplicial volume of a compact oriented 3-manifold. For p and q coprime, we show that the Chen–Yang volume conjecture is
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Classification of ℚ-Fano 3-folds of Gorenstein index 2 via key varieties constructed from projective bundles Int. J. Math. (IF 0.6) Pub Date : 2023-07-17 Hiromichi Takagi
We classified prime ℚ-Fano 3-folds X with only 1/2(1,1,1)-singularities and with h0(−KX)≥4 a long time ago. The classification was undertaken by blowing up each X at one 1/2(1,1,1)-singularity and constructing a Sarkisov link. In this paper, revealing the geometries behind the Sarkisov link for X in one of 5 classes, we show that X can be embedded as a linear section into a bigger dimensional ℚ-Fano