-
A note on the capacity estimate in metastability for generic configurations manuscripta math. (IF 0.6) Pub Date : 2024-04-08 Benny Avelin, Vesa Julin
-
Rigidity of bach-flat gradient schouten solitons manuscripta math. (IF 0.6) Pub Date : 2024-04-08 Valter Borges
In this paper, we show that complete Bach-flat Schouten solitons with \(n\ge 4\) are rigid. When \(n=3\) we are able to conclude rigidity under a more general condition, namely when the Bach tensor is divergence-free. These results imply rigidity of locally conformally flat Schouten solitons for \(n\ge 3\).
-
Local vanishing for toric varieties manuscripta math. (IF 0.6) Pub Date : 2024-04-06 Wanchun Shen, Sridhar Venkatesh, Anh Duc Vo
Let X be a toric variety. We establish vanishing (and non-vanishing) results for the sheaves \(R^if_*\Omega ^p_{\tilde{X}}(\log E)\), where \(f: \tilde{X} \rightarrow X\) is a strong log resolution of singularities with reduced exceptional divisor E. These extend the local vanishing theorem for toric varieties in Mustaţă et al. (J. Inst. Math. Jussieu 19(3):801-819, 2020). Our consideration of these
-
Abelian covers and the second fundamental form manuscripta math. (IF 0.6) Pub Date : 2024-04-04 Paola Frediani
-
Quasi-abelian group as automorphism group of Riemann surfaces manuscripta math. (IF 0.6) Pub Date : 2024-04-03 Rubén A. Hidalgo, Yerika L. Marín Montilla, Saúl Quispe
Conformal/anticonformal actions of the quasi-abelian group \(QA_{n}\) of order \(2^n\), for \(n\ge 4\), on closed Riemann surfaces, pseudo-real Riemann surfaces and closed Klein surfaces are considered. We obtain several consequences, such as the solution of the minimum genus problem for the \(QA_n\)-actions, and for each of these actions, we study the topological rigidity action problem. In the case
-
Some functional inequalities under lower Bakry–Émery–Ricci curvature bounds with $${\varepsilon }$$ -range manuscripta math. (IF 0.6) Pub Date : 2024-04-02 Yasuaki Fujitani
For n-dimensional weighted Riemannian manifolds, lower m-Bakry–Émery–Ricci curvature bounds with \({\varepsilon }\)-range, introduced by Lu-Minguzzi-Ohta (Anal Geom Metr Spaces 10(1):1–30, 2022), integrate constant lower bounds and certain variable lower bounds in terms of weight functions. In this paper, we prove a Cheng type inequality and a local Sobolev inequality under lower m-Bakry–Émery–Ricci
-
Iterated monodromy group of a PCF quadratic non-polynomial map manuscripta math. (IF 0.6) Pub Date : 2024-04-02 Özlem Ejder, Yasemin Kara, Ekin Ozman
We study the postcritically finite non-polynomial map \(f(x)=\frac{1}{(x-1)^2}\) over a number field k and prove various results about the geometric \(G^{\textrm{geom}}(f)\) and arithmetic \(G^{\textrm{arith}}(f)\) iterated monodromy groups of f. We show that the elements of \(G^{\textrm{geom}}(f)\) are the ones in \(G^{\textrm{arith}}(f)\) that fix certain roots of unity by assuming a conjecture on
-
Submanifolds with constant Moebius curvature and flat normal bundle manuscripta math. (IF 0.6) Pub Date : 2024-04-01 M. S. R. Antas, R. Tojeiro
We classify isometric immersions \(f:M^{n}\rightarrow \mathbb {R}^{n+p}\), \(n \ge 5\) and \(2p \le n\), with constant Moebius curvature and flat normal bundle.
-
Local Galois representations associated to additive polynomials manuscripta math. (IF 0.6) Pub Date : 2024-03-30 Takahiro Tsushima
For an additive polynomial and a positive integer, we define an irreducible smooth representation of a Weil group of a non-archimedean local field. We study several invariants of this representation. We obtain a necessary and sufficient condition for it to be primitive.
-
Desingularization of generic symmetric and generic skew-symmetric determinantal singularities manuscripta math. (IF 0.6) Pub Date : 2024-03-20 Sabrina Alexandra Gaube, Bernd Schober
We discuss how to resolve generic skew-symmetric and generic symmetric determinantal singularities. The key ingredients are (skew-) symmetry preserving matrix operations in order to deduce an inductive argument.
-
Weak approximation on Châtelet surfaces manuscripta math. (IF 0.6) Pub Date : 2024-03-18 Masahiro Nakahara, Samuel Roven
We study weak approximation for Châtelet surfaces over number fields when all singular fibers are defined over rational points. We consider Châtelet surfaces which satisfy weak approximation over every finite extension of the ground field. We prove many of these results by showing that the Brauer–Manin obstruction vanishes, then apply results of Colliot-Thélène, Sansuc, and Swinnerton-Dyer.
-
Liouville theorem for exponentially harmonic functions on Riemannian manifolds with compact boundary manuscripta math. (IF 0.6) Pub Date : 2024-03-16 Xinrong Jiang, Jianyi Mao
In this note, we derive a Yau type gradient estimate for positive exponentially harmonic functions on Riemannian manifolds with compact boundary. As its application, we obtain a Liouville type theorem.
-
Gromov hyperbolicity and unbounded uniform domains manuscripta math. (IF 0.6) Pub Date : 2024-03-16 Qingshan Zhou, Yuehui He, Antti Rasila, Tiantian Guan
-
Partial regularity for minimizers of a class of discontinuous Lagrangians manuscripta math. (IF 0.6) Pub Date : 2024-03-14 Roberto Colombo
We study a one-dimensional Lagrangian problem including the variational reformulation, derived in a recent work of Ambrosio–Baradat–Brenier, of the discrete Monge–Ampère gravitational model, which describes the motion of interacting particles whose dynamics is ruled by the optimal transport problem. The more general action-type functional we consider contains a discontinuous potential term related
-
Hodge numbers of O’Grady 6 via Ngô strings manuscripta math. (IF 0.6) Pub Date : 2024-03-13 Ben Wu
We give an alternative computation of the Betti and Hodge numbers for manifolds of OG6 type using the method of Ngô Strings introduced by de Cataldo, Rapagnetta, and Saccà.
-
Poisson commutative subalgebras associated with a Cartan subalgebra manuscripta math. (IF 0.6) Pub Date : 2024-03-13 Oksana S. Yakimova
Let \({\mathfrak g}\) be a reductive Lie algebra and \(\mathfrak t\subset \mathfrak g\) a Cartan subalgebra. The \(\mathfrak t\)-stable decomposition \({\mathfrak g}=\mathfrak t\oplus {\mathfrak m}\) yields a bi-grading of the symmetric algebra \({\mathcal {S}}({\mathfrak g})\). The subalgebra \({\mathcal {Z}}_{({\mathfrak g},\mathfrak t)}\) generated by the bi-homogenous components of the symmetric
-
Weights for compact connected Lie groups manuscripta math. (IF 0.6) Pub Date : 2024-03-09 Radha Kessar, Gunter Malle, Jason Semeraro
Let \(\ell \) be a prime. If \(\textbf{G}\) is a compact connected Lie group, or a connected reductive algebraic group in characteristic different from \(\ell \), and \(\ell \) is a good prime for \(\textbf{G}\), we show that the number of weights of the \(\ell \)-fusion system of \(\textbf{G}\) is equal to the number of irreducible characters of its Weyl group. The proof relies on the classification
-
Upper bounds for the critical values of homology classes of loops manuscripta math. (IF 0.6) Pub Date : 2024-03-02 Hans-Bert Rademacher
In this short note we discuss upper bounds for the critical values of homology classes in the based and free loop space of compact manifolds carrying a Riemannian or Finsler metric of positive Ricci curvature. In particular it follows that a shortest closed geodesic on a compact and simply-connected n-dimensional manifold of positive Ricci curvature \(\text {Ric}\ge n-1\) has length \(\le n \pi .\)
-
Diameter estimates for surfaces in conformally flat spaces manuscripta math. (IF 0.6) Pub Date : 2024-03-01 Marco Flaim, Christian Scharrer
-
Singular Yamabe problem for scalar flat metrics on the sphere manuscripta math. (IF 0.6) Pub Date : 2024-01-24 Aram L. Karakhanyan
Let \(\Omega \) be a domain on the unit n-sphere \( {\mathbb {S}}^n\) and \( \overset{{\,}_\circ }{g}\) the standard metric of \({\mathbb {S}}^n\), \(n\ge 3\). We show that there exists a conformal metric g with vanishing scalar curvature \(R(g)=0\) such that \((\Omega , g)\) is complete if and only if the Bessel capacity \({\mathcal {C}}_{\alpha , q}({\mathbb {S}}^n\setminus \Omega )=0\), where \(\alpha
-
Chern number inequalities of deformed Hermitian-Yang-Mills metrics on four dimensional Kähler manifolds manuscripta math. (IF 0.6) Pub Date : 2024-01-21 Xiaoli Han, Xishen Jin
In this paper, we give an affirmative answer to a conjecture of Collins-Yau [8]. We investigate the Chern number inequalities on 4-dimensional Kähler manifolds admitting the deformed Hermitian-Yang-Mills metrics under the assumption \({{\hat{\theta }}}\in (\pi ,2\pi )\).
-
Mass-growth of triangulated auto-equivalences manuscripta math. (IF 0.6) Pub Date : 2024-01-18 Jon Woolf
-
The string topology coproduct on complex and quaternionic projective space manuscripta math. (IF 0.6) Pub Date : 2024-01-18 Maximilian Stegemeyer
On the free loop space of compact symmetric spaces Ziller introduced explicit cycles generating the homology of the free loop space. We use these explicit cycles to compute the string topology coproduct on complex and quaternionic projective space. The behavior of the Goresky-Hingston product for these spaces then follows directly.
-
Weak Akizuki–Nakano vanishing theorem for singular globally F-split 3-folds manuscripta math. (IF 0.6) Pub Date : 2024-01-10 Kenta Sato, Shunsuke Takagi
In this paper, we prove that a weak form of the Akizuki–Nakano vanishing theorem holds on singular globally F-split 3-folds. Making use of this vanishing theorem, we study deformations of globally F-split Fano 3-folds and the Kodaira vanishing theorem for thickenings of locally complete intersection globally F-regular 3-folds.
-
Koszul property of Ulrich bundles and rationality of moduli spaces of stable bundles on Del Pezzo surfaces manuscripta math. (IF 0.6) Pub Date : 2024-01-09 Purnaprajna Bangere, Jayan Mukherjee, Debaditya Raychaudhury
Let \({\mathscr {E}}\) be a vector bundle on a smooth projective variety \(X\subseteq {\mathbb {P}}^N\) that is Ulrich with respect to the hyperplane section H. In this article, we study the Koszul property of \({\mathscr {E}}\), the slope-semistability of the k-th iterated syzygy bundle \({\mathscr {S}}_k({\mathscr {E}})\) for all \(k\ge 0\) and rationality of moduli spaces of slope-stable bundles
-
Characterizations of Fano type varieties and projective spaces via absolute complexity manuscripta math. (IF 0.6) Pub Date : 2024-01-04 Dae-Won Lee
In this paper, we obtain several characterizations of varieties of Fano type and projective spaces via absolute complexity. Also, we show that if the absolute complexity of a given pair \((X,\Delta )\) is negative, then the pair \((X,\Delta )\) does not admit any \(-(K_X+\Delta )\)-minimal models.
-
Estimates for the average scalar curvature of the Weil–Petersson metric on the moduli space $${\overline{{{\mathcal {M}}} }}_g$$ manuscripta math. (IF 0.6) Pub Date : 2023-12-10 Georg Schumacher, Stefano Trapani
We give a precise estimate for the average scalar curvature of the Weil–Petersson metric on the moduli space \({\overline{{{\mathcal {M}}} }}_g\) as \(g\rightarrow \infty \) up to the order \(1/g^2\).
-
Zeta function of some Kummer Calabi-Yau 3-folds manuscripta math. (IF 0.6) Pub Date : 2023-12-07 Dominik Burek
We compute Hodge numbers and zeta function of a Kummer Calabi-Yau 3-folds introduced by M. Andreatta and J. Wiśniewski in [2] and investigated by M. Donten-Bury in [13].
-
-
Shifting numbers of abelian varieties via bounded t-structures manuscripta math. (IF 0.6) Pub Date : 2023-11-27 Yu-Wei Fan
The shifting numbers measure the asymptotic amount by which an endofunctor of a triangulated category translates inside the category, and are analogous to Poincaré translation numbers that are widely used in dynamical systems. Motivated by this analogy, Fan–Filip raised the following question: “Do the shifting numbers define a quasimorphism on the group of autoequivalences of a triangulated category
-
The Dirichlet problem for prescribed curvature equations of p-convex hypersurfaces manuscripta math. (IF 0.6) Pub Date : 2023-11-17 Weisong Dong
In this paper, we study the Dirichlet problem for p-convex hypersurfaces with prescribed curvature. We prove that there exists a graphic hypersurface satisfying the prescribed curvature equation with homogeneous boundary condition. An interior curvature estimate is also obtained.
-
Polyharmonic surfaces in 3-dimensional homogeneous spaces manuscripta math. (IF 0.6) Pub Date : 2023-11-13 S. Montaldo, C. Oniciuc, A. Ratto
-
Cuspidal components of Siegel modular forms for large discrete series representations of $$\textrm{Sp}_4({\mathbb {R}})$$ manuscripta math. (IF 0.6) Pub Date : 2023-11-13 Shuji Horinaga, Hiro-aki Narita
In this paper, we consider automorphic forms on \(\textrm{Sp}_4({\mathbb {A}}_{\mathbb {Q}})\) which generate large discrete series representations of \(\textrm{Sp}_4({\mathbb {R}})\) as \((\mathfrak {sp}_4({\mathbb {R}}),K_\infty )\)-modules. We determine the cuspidal components and the structure of the space of such automorphic forms.
-
On algebraic Chern classes of flat vector bundles manuscripta math. (IF 0.6) Pub Date : 2023-11-09 Adrian Langer
-
Existence of self-similar Dirichlet forms on post-critically finite fractals in terms of their resistances manuscripta math. (IF 0.6) Pub Date : 2023-11-09 Guanhua Liu
-
On the rationality of certain Fano threefolds manuscripta math. (IF 0.6) Pub Date : 2023-11-06 Ciro Ciliberto
In this paper we study the rationality problem for Fano threefolds \(X\subset {\mathbb P}^{p+1}\) of genus p, that are Gorenstein, with at most canonical singularities. The main results are: (1) a trigonal Fano threefold of genus p is rational as soon as \(p\geqslant 8\) (this result has already been obtained in Przyjalkowski et al. (Izv Math 69(2):365–421, 2005), but we give here an independent proof);
-
Boundedness of regular del Pezzo surfaces over imperfect fields manuscripta math. (IF 0.6) Pub Date : 2023-10-30 Hiromu Tanaka
For a regular del Pezzo surface X, we prove that \(|-12K_X|\) is very ample. Furthermore, we also give an explicit upper bound for the volume \(K_X^2\) which depends only on \([k: k^p]\) for the base field k. As a consequence, we obtain the boundedness of geometrically integral regular del Pezzo surfaces.
-
Formal ternary laws and Buchstaber’s 2-groups manuscripta math. (IF 0.6) Pub Date : 2023-10-30 David Coulette, Frédéric Déglise, Jean Fasel, Jens Hornbostel
We compare formal ternary laws to Buchstaber’s 2-valued formal group laws, by means of explicit functors. We also provide a few computations of formal ternary laws of low complexity degree.
-
Bounds for GL $$_2$$ $$\times $$ GL $$_2$$ L-functions in the depth aspect manuscripta math. (IF 0.6) Pub Date : 2023-10-28 Qingfeng Sun
Let f and g be holomorphic or Maass cusp forms for \(\mathrm SL_2({\mathbb {Z}})\) and let \(\chi \) be a primitive Dirichlet character of prime power conductor \(R=p^{\kappa }\) with p an odd prime and \(\kappa >12\). A subconvex bound for the central values of the Rankin–Selberg L-functions \(L(s,f\otimes g \otimes \chi )\) is proved in the depth aspect $$\begin{aligned} L\left( \frac{1}{2},f\otimes
-
On classic n-universal quadratic forms over dyadic local fields manuscripta math. (IF 0.6) Pub Date : 2023-10-24 Zilong He
Let n be an integer and \( n\ge 2 \). A classic integral quadratic form over local fields is called classic n-universal if it represents all n-ary classic integral quadratic forms. We determine the equivalent conditions and minimal testing sets for classic n-universal quadratic forms over dyadic local fields.
-
Moduli of Lie p-algebras manuscripta math. (IF 0.6) Pub Date : 2023-10-05 Alice Bouillet
In this paper, we study moduli spaces of finite-dimensional Lie algebras with flat center, proving that the forgetful map from Lie p-algebras to Lie algebras is an affine fibration, and we point out a new case of existence of a p-mapping. Then we illustrate these results for the special case of Lie algebras of rank 3, whose moduli space we build and study over \(\mathbb {Z}\). We extend the classical
-
On a microlocal version of Young’s product theorem manuscripta math. (IF 0.6) Pub Date : 2023-09-24 Claudio Dappiaggi, Paolo Rinaldi, Federico Sclavi
A key result in distribution theory is Young’s product theorem which states that the product between two Hölder distributions \(u\in \mathcal {C}^\alpha (\mathbb {R}^d)\) and \(v\in \mathcal {C}^\beta (\mathbb {R}^d)\) can be unambiguously defined if \(\alpha +\beta >0\). We revisit the problem of multiplying two Hölder distributions from the viewpoint of microlocal analysis, using techniques proper
-
The global behaviors for defocusing wave equations in two dimensional exterior region manuscripta math. (IF 0.6) Pub Date : 2023-09-18 Wei Dai
We study the defocusing semilinear wave equation in \({\mathbb {R}}\times {\mathbb {R}}^2\backslash {{\mathcal {K}}}\) with the Dirichlet boundary condition, where \({{\mathcal {K}}}\) is a star-shaped obstacle with smooth boundary. We first show that the potential energy of the solution will decay appropriately. Based on it, we show that the solution also pointwisely decays to 0. Finally, we show
-
Le Laplacien conforme sur les 2-tenseurs symétriques manuscripta math. (IF 0.6) Pub Date : 2023-09-13 Erwann Delay
On any riemannian manifolds, we explicit the conformally covariant Laplacian, acting on all (fields of) covariant symmetric tensor of order two. The latter being so far expressed only on Einstein manifold and acting simply on 2-tensors without trace and with zero divergence (TT-tensors).
-
Non-big Ulrich bundles: the classification on quadrics and the case of small numerical dimension manuscripta math. (IF 0.6) Pub Date : 2023-09-05 Angelo Felice Lopez, Roberto Muñoz, José Carlos Sierra
On any smooth n-dimensional variety we give a pretty precise picture of rank r Ulrich vector bundles with numerical dimension at most \(\frac{n}{2}+r-1\). Also, we classify non-big Ulrich vector bundles on quadrics and on the Del Pezzo fourfold of degree 6.
-
A motivic interpretation of Whittaker periods for $$\textrm{GL}_n$$ manuscripta math. (IF 0.6) Pub Date : 2023-08-29 Takashi Hara, Kenichi Namikawa
Admitting the existence of conjectural motives attached to cohomological irreducible cuspidal automorphic representations of \(\textrm{GL}_n\), we write down Raghuram and Shahidi’s Whittaker periods in terms of Yoshida’s fundamental periods when the base field is a totally real number field or a CM field.
-
On some rigidity theorems of Q-curvature manuscripta math. (IF 0.6) Pub Date : 2023-08-28 Yiyan Xu, Shihong Zhang
-
Einstein-like metrics on compact homogeneous spaces manuscripta math. (IF 0.6) Pub Date : 2023-08-27 Feng Li, Huibin Chen, Zhiqi Chen
In this paper, we study Einstein-like metrics on compact homogeneous spaces G/H. In the beginning, we give a characterization of Einstein-like metrics on compact homogeneous spaces. As an application, we classify all invariant Einstein-like metrics on compact homogeneous spaces with two isotropy summands and generalized Wallach spaces of exceptional type.
-
Weighted isoperimetric problem for spacelike hypersurface in de Sitter space manuscripta math. (IF 0.6) Pub Date : 2023-08-23 Kuicheng Ma
In this paper, we obtain the long-time existence and convergence results for a locally constrained mean curvature flow, which is nicely suitable for weighted isoperimetric problem. Using the maximum principle for tensors developed by Andrews, we show the preservation of some pinching condition along the considered flow and as an application we established the weighted isoperimetric inequality for pinched
-
Stable Ulrich bundles on cubic fourfolds manuscripta math. (IF 0.6) Pub Date : 2023-08-23 Truong Le Hoang, Yen Ngoc Hoang
In this paper, we examine the presence of Ulrich bundles on cubic fourfolds. We establish necessary and sufficient conditions for the existence of Ulrich bundles of a specific rank r. As a consequence, we show the existence of a family of non-decomposable Ulrich bundles of rank r on certain cubic fourfolds, which are dependent on approximately r parameters and have wild representation type. Our study
-
ACC of PLC threshold manuscripta math. (IF 0.6) Pub Date : 2023-08-22 Sung Rak Choi, Sungwook Jang
In this paper, we define the potential log canonical threshold and prove the ascending chain condition of the set of these thresholds satisfies. We also consider collections of Fano type varieties and study their basic properties including boundedness.
-
On Riemannian polyhedra with non-obtuse dihedral angles in 3-manifolds with positive scalar curvature manuscripta math. (IF 0.6) Pub Date : 2023-08-22 Li Yu
-
On the regularity and existence of weak solutions for a class of degenerate singular elliptic problem manuscripta math. (IF 0.6) Pub Date : 2023-08-19 Prashanta Garain
In this article, we consider a class of degenerate singular problems. The degeneracy is captured by the presence of a class of p-admissible weights, which may vanish or blow up near the origin. Further, the singularity is allowed to vary inside the domain. We provide sufficient conditions on the weight function, on the singular exponent and the source function to establish regularity and existence
-
The 3-dimensional Lyness map and a self-mirror log Calabi–Yau 3-fold manuscripta math. (IF 0.6) Pub Date : 2023-08-03 Tom Ducat
-
Integral points on symmetric affine cubic surfaces manuscripta math. (IF 0.6) Pub Date : 2023-08-02 H. Uppal
-
A general framework for tropical differential equations manuscripta math. (IF 0.6) Pub Date : 2023-07-27 Jeffrey Giansiracusa, Stefano Mereta
-
Almost complex parallelizable manifolds: Kodaira dimension and special structures manuscripta math. (IF 0.6) Pub Date : 2023-07-20 Andrea Cattaneo, Antonella Nannicini, Adriano Tomassini
We study the Kodaira dimension of a real parallelizable manifold M, with an almost complex structure J in standard form with respect to a given parallelism. For \(X = (M, J)\) we give conditions under which \({{\,\textrm{kod}\,}}(X) = 0\). We provide examples in the case \(M = G \times G\), where G is a compact connected real Lie group. Finally we describe geometrical properties of real parallelizable
-
Equivariant Grothendieck ring of a complete symmetric variety of minimal rank manuscripta math. (IF 0.6) Pub Date : 2023-07-15 V. Uma
We describe the G-equivariant Grothendieck ring of a regular compactification X of an adjoint symmetric space G/H of minimal rank. This extends the results of Brion and Joshua for the equivariant Chow ring of wonderful symmetric varieties of minimal rank in (Brion, M., Joshua, R. 13, 471–493 (2008)) and generalizes the results on the regular compactification of an adjoint semisimple group in (Uma,
-
Proof of Vogan’s conjecture on Arthur packets: irreducible parameters of p-adic general linear groups manuscripta math. (IF 0.6) Pub Date : 2023-07-14 Clifton Cunningham, Mishty Ray
-
An arithmetic valuative criterion for proper maps of tame algebraic stacks manuscripta math. (IF 0.6) Pub Date : 2023-07-03 Giulio Bresciani, Angelo Vistoli