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The twisted 1-loop invariant and the Jacobian of Ptolemy varieties Math. Z. (IF 0.8) Pub Date : 2024-04-26 Seokbeom Yoon
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On the Brauer groups of fibrations Math. Z. (IF 0.8) Pub Date : 2024-04-26 Yanshuai Qin
Let \({\mathcal {X}}\rightarrow C\) be a flat k-morphism between smooth integral varieties over a finitely generated field k such that the generic fiber X is smooth, projective and geometrically connected. Assuming that C is a curve with function field K, we build a relation between the Tate-Shafarevich group of \(\textrm{Pic}^0_{X/K}\) and the geometric Brauer groups of \({\mathcal {X}}\) and X, generalizing
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On the dynamic asymptotic dimension of étale groupoids Math. Z. (IF 0.8) Pub Date : 2024-04-26 Christian Bönicke
We investigate the dynamic asymptotic dimension for étale groupoids introduced by Guentner, Willett and Yu. In particular, we establish several permanence properties, including estimates for products and unions of groupoids. We also establish invariance of the dynamic asymptotic dimension under Morita equivalence. In the second part of the article, we consider a canonical coarse structure on an étale
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A remark on a weighted version of Suita conjecture for higher derivatives Math. Z. (IF 0.8) Pub Date : 2024-04-26 Qi’an Guan, Xun Sun, Zheng Yuan
In this article, we consider the set of points for the holding of the equality in a weighted version of Suita conjecture for higher derivatives, and give relations between the set and the integer valued points of a class of harmonic functions (maybe multi-valued). For planar domains bounded by finite analytic closed curves, we give relations between the set and Dirichlet problem.
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Remarks on the existence of minimal models of log canonical generalized pairs Math. Z. (IF 0.8) Pub Date : 2024-04-26 Nikolaos Tsakanikas, Lingyao Xie
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On multipliers into martingale $$SL^\infty $$ spaces for arbitrary filtrations Math. Z. (IF 0.8) Pub Date : 2024-04-21 Anton Tselishchev
In this paper we study the following problem: for a given bounded positive function f on a filtered probability space can we find another function (a multiplier) m, \(0\le m\le 1\), such that the function mf is not “too small” but its square function is bounded? We explicitly show how to construct such multipliers for the usual martingale square function and for so-called conditional square function
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Bott vanishing for Fano threefolds Math. Z. (IF 0.8) Pub Date : 2024-04-20 Burt Totaro
Bott proved a strong vanishing theorem for sheaf cohomology on projective space, namely that \(H^j(X,\Omega ^i_X\otimes L)=0\) for \(j>0\), \(i\ge 0\), and L ample. This holds for toric varieties, but not for most other varieties. We classify the smooth Fano threefolds that satisfy Bott vanishing. There are many more than expected.
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Shape optimization for combinations of Steklov eigenvalues on Riemannian surfaces Math. Z. (IF 0.8) Pub Date : 2024-04-15 Romain Petrides
We prove existence and regularity of metrics which minimize combinations of Steklov eigenvalues over metrics of unit perimeter on a surface with boundary. We show that there are free boundary minimal immersions into ellipsoids parametrized by eigenvalues, such that the coordinate functions are eigenfunctions with respect to the minimal metrics. This work generalizes Fraser–Schoen’s and the author’s
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Simples in a cotilting heart Math. Z. (IF 0.8) Pub Date : 2024-04-13 Lidia Angeleri Hügel, Ivo Herzog, Rosanna Laking
Every cotilting module over a ring R induces a t-structure with a Grothendieck heart in the derived category D(Mod-R). We determine the simple objects in this heart and their injective envelopes, combining torsion-theoretic aspects with methods from the model theory of modules and Auslander-Reiten theory.
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Locally free Caldero–Chapoton functions via reflections Math. Z. (IF 0.8) Pub Date : 2024-04-12 Lang Mou
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Unfolding and injectivity of the Kudla–Millson lift of genus 1 Math. Z. (IF 0.8) Pub Date : 2024-04-12 Riccardo Zuffetti
We unfold the theta integrals defining the Kudla–Millson lift of genus 1 associated to even lattices of signature (b, 2), where \(b>2\). This enables us to compute the Fourier expansion of such defining integrals and prove the injectivity of the Kudla–Millson lift. Although the latter result has been already proved in [5], our new procedure has the advantage of paving the ground for a strategy to prove
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Asymptotic strictly pseudoconvex CR structure for asymptotically locally complex hyperbolic manifolds Math. Z. (IF 0.8) Pub Date : 2024-04-10 Alan Pinoy
In this paper, we build a compactification by a strictly pseudoconvex CR structure for a complete and non-compact Kähler manifold whose curvature tensor is asymptotic to that of the complex hyperbolic space. To do so, we study in depth the evolution of various geometric objects that are defined on the leaves of some foliation of the complement of a suitable convex subset, called an essential subset
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Itoh’s conjecture for normal ideals Math. Z. (IF 0.8) Pub Date : 2024-04-10 Tony J. Puthenpurakal
Let \((A,\mathfrak {m} )\) be an analytically unramified Cohen–Macaulay local ring and let \(\mathfrak {a} \) be an \(\mathfrak {m} \)-primary ideal in A. If I is an ideal in A then let \(I^*\) be the integral closure of I in A. Let \(G_{\mathfrak {a}}(A) ^* = \bigoplus _{n\ge 0 }(\mathfrak {a} ^n)^*/(\mathfrak {a} ^{n+1})^*\) be the associated graded ring of the integral closure filtration of \(\mathfrak
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Lefschetz-type theorems for the effective cone on Hyperkähler varieties Math. Z. (IF 0.8) Pub Date : 2024-04-10 Jonas Baltes
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Non-locally discrete actions on the circle with at most N fixed points Math. Z. (IF 0.8) Pub Date : 2024-04-08 Christian Bonatti, João Carnevale, Michele Triestino
A subgroup of \(\textrm{Homeo}_+(\mathbb {S}^1)\) is Möbius-like if every element is conjugate to an element of \(\textrm{PSL}(2,\mathbb {R})\). In general, a Möbius-like subgroup of \(\textrm{Homeo}_+(\mathbb {S}^1)\) is not necessarily (semi-)conjugate to a subgroup of \(\textrm{PSL}(2,\mathbb {R})\), as discovered by Kovačević (Trans Am Math Soc 351:4823–4835, 1999). Here we determine simple dynamical
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Kählerity of Einstein four-manifolds Math. Z. (IF 0.8) Pub Date : 2024-04-08 Xiaolong Li, Yongjia Zhang
We prove that a closed oriented Einstein four-manifold is either anti-self-dual or (after passing to a double Riemannian cover if necessary) Kähler–Einstein, provided that \(\lambda _2 \ge -\frac{S}{12}\), where \(\lambda _2\) is the middle eigenvalue of the self-dual Weyl tensor \(W^+\) and S is the scalar curvature. An analogous result holds for closed oriented four-manifolds with \(\delta W^+=0\)
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Periodic solutions to second-order differential equations with fading memory Math. Z. (IF 0.8) Pub Date : 2024-04-08 Rodrigo Ponce
We characterize existence and uniqueness of periodic strong and mild solutions to an abstract second order differential equation with memory in Banach spaces. Using vector-valued Fourier multipliers we give necessary and sufficient conditions in order to ensure the well-posedness of this equation in Lebesgue, Hölder and Besov spaces.
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Stability of kernel sheaves associated to rank one torsion-free sheaves Math. Z. (IF 0.8) Pub Date : 2024-04-04 Nick Rekuski
We show the kernel sheaf associated to a sufficiently positive torsion-free sheaf of rank one is slope stable. Furthermore, we are able to give an explicit bound for “sufficiently positive.” This settles a conjecture of Ein–Lazarsfeld–Mustopa. The main technical lemma is a bound on the number of global sections of a globally generated, torsion-free sheaf in terms of its rank, degree, and invariants
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Uniform a priori estimates for the n-th order Lane–Emden system in $$\mathbb {R}^{n}$$ with $$n\ge 3$$ Math. Z. (IF 0.8) Pub Date : 2024-04-04
Abstract In this paper, we establish uniform a priori estimates for positive solutions to the (higher) critical order superlinear Lane–Emden system in bounded domains with Navier boundary conditions in arbitrary dimensions \(n\ge 3\) . First, we prove the monotonicity of solutions for odd order (higher order fractional system) and even order system (integer order system) respectively along the inward
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Random group actions on $$\textrm{CAT}(0)$$ square complexes Math. Z. (IF 0.8) Pub Date : 2024-03-25 Zachary Munro
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Twisted conformal blocks and their dimension Math. Z. (IF 0.8) Pub Date : 2024-03-19 Jiuzu Hong, Shrawan Kumar
Let \(\Gamma \) be a finite group acting on a simple Lie algebra \({\mathfrak {g}}\) and acting on a s-pointed projective curve \((\Sigma , \vec {p}=\{p_1, \ldots , p_s\})\) faithfully (for \(s\ge 1\)). Also, let an integrable highest weight module \({\mathscr {H}}_c(\lambda _i)\) of an appropriate twisted affine Lie algebra determined by the ramification at \(p_i\) with a fixed central charge c is
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Global $$\textbf{B}(G)$$ with adelic coefficients and transfer factors at non-regular elements Math. Z. (IF 0.8) Pub Date : 2024-03-15 Alexander Bertoloni Meli
The goal of this paper is extend Kottwitz’s theory of B(G) for global fields. In particular, we show how to extend the definition of “B(G) with adelic coefficients” from tori to all connected reductive groups. As an application, we give an explicit construction of certain transfer factors for non-regular semisimple elements of non-quasisplit groups. This generalizes some results of Kaletha and Taibi
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Ill-posedness for the Half wave Schrödinger equation Math. Z. (IF 0.8) Pub Date : 2024-03-15 Isao Kato
We study the Cauchy problem for the half wave Schrödinger equation introduced by Xu [9]. There are some well-posedness results for the equation, however there is no ill-posedness result. We focus on the scale critical space and obtain the ill-posedness in the super-critical or at the critical space under certain condition. The proofs in the super-critical space are based on the argument established
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Bloom weighted bounds for sparse forms associated to commutators Math. Z. (IF 0.8) Pub Date : 2024-03-15 Andrei K. Lerner, Emiel Lorist, Sheldy Ombrosi
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Jordan mating is always possible for polynomials Math. Z. (IF 0.8) Pub Date : 2024-03-15
Abstract Suppose f and g are two post-critically finite polynomials of degree \(d_1\) and \(d_2\) respectively and suppose both of them have a finite super-attracting fixed point of degree \(d_0\) . We prove that one can always construct a rational map R of degree $$\begin{aligned} D = d_1 + d_2 - d_0 \end{aligned}$$ by gluing f and g along the Jordan curve boundaries of the immediate super-attracting
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D-finiteness, rationality, and height III: multivariate Pólya–Carlson dichotomy Math. Z. (IF 0.8) Pub Date : 2024-03-14 Jason P. Bell, Shaoshi Chen, Khoa D. Nguyen, Umberto Zannier
We prove a result that can be seen as an analogue of the Pólya–Carlson theorem for multivariate D-finite power series with coefficients in \(\bar{\mathbb {Q}}\). In the special case that the coefficients are algebraic integers, our main result says that if $$\begin{aligned} F(x_1,\ldots ,x_m)=\sum f(n_1,\ldots ,n_m)x_1^{n_1}\cdots x_m^{n_m} \end{aligned}$$ is a D-finite power series in m variables
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Cohomology and geometry of Deligne–Lusztig varieties for $$\textrm{GL}_n$$ Math. Z. (IF 0.8) Pub Date : 2024-03-14 Yingying Wang
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Matrix Kloosterman sums modulo prime powers Math. Z. (IF 0.8) Pub Date : 2024-03-14 M. Erdélyi, Á. Tóth, G. Zábrádi
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A note on the semistability of singular projective hypersurfaces Math. Z. (IF 0.8) Pub Date : 2024-03-14 Thomas Mordant
In this note, we give sufficient conditions for the (semi)stability of a hypersurface H of \(\mathbb {P}^N_k\) in terms of its degree d, the maximal multiplicity \(\delta \) of its singularities, and the dimension s of its singular locus. For instance, we show that H is semistable when \(d \ge \delta \min (N+1, s+3)\). The proof relies in particular on Benoist’s lower bound for the dimension of the
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Canonical integral operators on the Fock space Math. Z. (IF 0.8) Pub Date : 2024-03-12 Xingtang Dong, Kehe Zhu
In this paper we introduce and study a two-parameter family of integral operators on the Fock space \(F^2({\mathbb {C}})\). We determine exactly when these operators are bounded and when they are unitary. We show that, under the Bargmann transform, these operators include the classical linear canonical transforms as special cases. As an application, we obtain a new unitary projective representation
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Nonempty interior of configuration sets via microlocal partition optimization Math. Z. (IF 0.8) Pub Date : 2024-03-12 Allan Greenleaf, Alex Iosevich, Krystal Taylor
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Whittaker categories and the minimal nilpotent finite W-algebras for $$\mathfrak {sl}_{n+1}$$ Math. Z. (IF 0.8) Pub Date : 2024-03-12 Genqiang Liu, Yang Li
For any \({\textbf{a}}=(a_1,\dots ,a_n)\in {\mathbb {C}}^n\), we introduce a Whittaker category \({\mathcal {H}}_{{\textbf{a}}}\) whose objects are \(\mathfrak {sl}_{n+1}\)-modules M such that \(e_{0i}-a_i\) acts locally nilpotently on M for all \(i \in \{1,\dots ,n\}\), and the subspace \(\textrm{wh}_{{\textbf{a}}}(M)=\{v\in M \mid e_{0i} v=a_iv, \ i=1,\dots ,n\}\) is finite dimensional. In this paper
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$$L^{\vec {p}}-L^{\vec {q}}$$ boundedness of multiparameter Forelli–Rudin type operators on the product of unit balls of $${\mathbb {C}}^n$$ Math. Z. (IF 0.8) Pub Date : 2024-03-09 Long Huang, Xiaofeng Wang, Zhicheng Zeng
In this work, we provide a complete characterization of the boundedness of two classes of multiparameter Forelli–Rudin type operators from one mixed-norm Lebesgue space \(L^{{\vec {p}}}\) to another space \(L^{{\vec {q}}}\), when \(1\le \vec {p}\le {\vec {q}}<\infty \), equipped with possibly different weights. Using these characterizations, we establish the necessary and sufficient conditions for
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Rank-one perturbations and norm-attaining operators Math. Z. (IF 0.8) Pub Date : 2024-03-08
Abstract The main goal of this article is to show that for every (reflexive) infinite-dimensional Banach space X there exists a reflexive Banach space Y and \(T, R \in \mathcal {L}(X,Y)\) such that R is a rank-one operator, \(\Vert T+R\Vert >\Vert T\Vert \) but \(T+R\) does not attain its norm. This answers a question posed by Dantas and the first two authors. Furthermore, motivated by the parallelism
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Greatest common divisors for polynomials in almost units and applications to linear recurrence sequences Math. Z. (IF 0.8) Pub Date : 2024-03-08
Abstract We bound the greatest common divisor of two coprime multivariable polynomials evaluated at algebraic numbers, generalizing work of Levin, and going towards conjectured inequalities of Silverman and Vojta. As an application, we prove results on greatest common divisors of terms from two linear recurrence sequences, extending the results of Levin, who considered the case where the linear recurrences
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On inverted Kloosterman sums over finite fields Math. Z. (IF 0.8) Pub Date : 2024-03-07 Xin Lin, Daqing Wan
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The jump problem for the critical Besov space Math. Z. (IF 0.8) Pub Date : 2024-03-07 Tailiang Liu, Yuliang Shen
We introduce the critical Besov space \( B_{p} \) on quasicircles and prove the solvability of the jump problem on d-regular quasicircles with \( B_{p} \) boundary values for \( d
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Fox–Neuwirth cells, quantum shuffle algebras, and the homology of type-B Artin groups Math. Z. (IF 0.8) Pub Date : 2024-03-06 Anh Trong Nam Hoang
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Global endpoint regularity estimates for the fractional Dirichlet problem Math. Z. (IF 0.8) Pub Date : 2024-03-06 Wenxian Ma, Sibei Yang
Let \(n\ge 2\), \(s\in (0,1)\), and \(\Omega \subset {\mathbb {R}}^n\) be a bounded \(C^2\) domain. The aim of this paper is to study the global endpoint regularity estimates for the fractional Dirichlet problem $$\begin{aligned} {\left\{ \begin{array}{ll} (-\Delta )^su=f \ \ {} &{} \text {in}\ \ \Omega ,\\ u=0 \ \ {} &{} \text {in}\ \ {\mathbb {R}}^n\setminus \Omega . \end{array}\right. } \end{aligned}$$
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Generic vanishing, 1-forms, and topology of Albanese maps Math. Z. (IF 0.8) Pub Date : 2024-02-27 Yajnaseni Dutta, Feng Hao, Yongqiang Liu
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Quaternionic slice regularity beyond slice domains Math. Z. (IF 0.8) Pub Date : 2024-02-26 Riccardo Ghiloni, Caterina Stoppato
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Refinements to the prime number theorem for arithmetic progressions Math. Z. (IF 0.8) Pub Date : 2024-02-20 Jesse Thorner, Asif Zaman
We prove a version of the prime number theorem for arithmetic progressions that is uniform enough to deduce the Siegel–Walfisz theorem, Hoheisel’s asymptotic for intervals of length \(x^{7/12+\varepsilon }\), a Brun–Titchmarsh bound, and Linnik’s bound on the least prime in an arithmetic progression as corollaries. Our proof uses the Vinogradov–Korobov zero-free region, a log-free zero density estimate
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$$\ell ^1$$ -summability and Fourier series of B-splines with respect to their knots Math. Z. (IF 0.8) Pub Date : 2024-02-17 Martin Buhmann, Janin Jäger, Yuan Xu
We study the \(\ell ^1\)-summability of functions in the d-dimensional torus \({{\mathbb {T}}}^d\) and so-called \(\ell ^1\)-invariant functions. Those are functions on the torus whose Fourier coefficients depend only on the \(\ell ^1\)-norm of their indices. Such functions are characterized as divided differences that have \(\cos {\theta }_1,\ldots ,\cos {\theta }_d\) as knots for \(({\theta }_1\
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Multiple normalized solutions for the planar Schrödinger–Poisson system with critical exponential growth Math. Z. (IF 0.8) Pub Date : 2024-02-16 Sitong Chen, Vicenţiu D. Rădulescu, Xianhua Tang
The paper deals with the existence of normalized solutions for the following Schrödinger–Poisson system with \(L^2\)-constraint: $$\begin{aligned} \left\{ \begin{array}{ll} -\Delta u+\lambda u+\mu \left( \log |\cdot |*u^2\right) u=\left( e^{u^2}-1-u^2\right) u, &{} x\in {\mathbb {R}}^2, \\ \int _{{\mathbb {R}}^2}u^2\textrm{d}x=c, \\ \end{array} \right. \end{aligned}$$ where \(\mu >0\), \(\lambda \in
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Talbot effect on the sphere and torus for $$d\ge 2$$ Math. Z. (IF 0.8) Pub Date : 2024-02-16 M. Burak Erdoğan, Chi N. Y. Huynh, Ryan McConnell
We utilize exponential sum techniques to obtain upper and lower bounds for the fractal dimension of the graph of solutions to the linear Schrödinger equation on \(\mathbb {S}^d\) and \(\mathbb {T}^d\). Specifically for \(\mathbb S^d\), we provide dimension bounds using both \(L^p\) estimates of Littlewood-Paley blocks, as well as assumptions on the Fourier coefficients. In the appendix, we present
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Isometries in the symmetrized bidisc Math. Z. (IF 0.8) Pub Date : 2024-02-16 Armen Edigarian
We provide a characterization of isometries in the sense of the Carathéodory–Reiffen metric in the symmetrized bidisc.
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Rational points on generic marked hypersurfaces Math. Z. (IF 0.8) Pub Date : 2024-02-14 Qixiao Ma
Over fields of characteristic zero, we show that for \(n=1,d\ge 4\) or \(n=2,d\ge 5\) or \(n\ge 3, d\ge 2n\), the generic m-marked degree-d hypersurface in \(\mathbb {P}^{n+1}\) admits the m marked points as all the rational points. Over arbitrary fields, we show that for \(n=1,d\ge 4\) or \(n\ge 2, d\ge 2n+3\), the identity map is the only rational self-map of the generic degree-d hypersurface in
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Desingularization of binomial varieties using toric Artin stacks Math. Z. (IF 0.8) Pub Date : 2024-02-14 Dan Abramovich, Bernd Schober
We show how the notion of fantastacks can be used to effectively desingularize binomial varieties defined over algebraically closed fields. In contrast to a desingularization via blow-ups in smooth centers, we drastically reduce the number of steps and the number of charts appearing along the process. Furthermore, we discuss how our considerations extend to a partial simultaneous normal crossings desingularization
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Positivity of extensions of vector bundles Math. Z. (IF 0.8) Pub Date : 2024-02-13
Abstract In this paper, we study when positivity conditions of vector bundles are preserved by extension. We prove that an extension of a big (resp. pseudo-effective) line bundle by an ample (resp. a nef) vector bundle is big (resp. pseudo-effective). We also show that an extension of an ample line bundle by a big line bundle is not necessarily pseudo-effective. In particular, this implies that an
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K-theory of relative group $$C^*$$ -algebras and the relative Novikov conjecture Math. Z. (IF 0.8) Pub Date : 2024-02-12 Jintao Deng, Geng Tian, Zhizhang Xie, Guoliang Yu
The relative Novikov conjecture states that the relative higher signatures of manifolds with boundary are invariant under orientation-preserving homotopy equivalences of pairs. The relative Baum–Connes assembly encodes information about the relative higher index of elliptic operators on manifolds with boundary. In this paper, we study the relative Baum–Connes assembly map for any pair of groups and
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Parabolic John–Nirenberg spaces with time lag Math. Z. (IF 0.8) Pub Date : 2024-02-12 Kim Myyryläinen, Dachun Yang
We introduce a parabolic version of the so-called John–Nirenberg space that is a generalization of functions of parabolic bounded mean oscillation. Parabolic John–Nirenberg inequalities, which give weak type estimates for the oscillation of a function, are shown in the setting of the parabolic geometry with a time lag. Our arguments are based on a parabolic Calderón–Zygmund decomposition and a good
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Almost nonnegative Ricci curvature and new vanishing theorems for genera Math. Z. (IF 0.8) Pub Date : 2024-02-10 Xiaoyang Chen, Jian Ge, Fei Han
We derive new vanishing theorems for genera under almost nonnegative Ricci curvature and infinite fundamental group. A vanishing theorem of Euler characteristic number for almost nonnegatively curved Alexandrov spaces is also proved.
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On the distribution of modular square roots of primes Math. Z. (IF 0.8) Pub Date : 2024-02-10 Ilya D. Shkredov, Igor E. Shparlinski, Alexandru Zaharescu
We use recent bounds on bilinear sums with modular square roots to study the distribution of solutions to congruences \(x^2 \equiv p \pmod q\) with primes \(p\leqslant P\) and \(q \leqslant Q\). This can be considered as a combined scenario of Duke, Friedlander and Iwaniec with averaging only over the modulus q and of Dunn, Kerr, Shparlinski and Zaharescu with averaging only over p.
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Quasisymmetric maps, shears, lambda lengths and flips Math. Z. (IF 0.8) Pub Date : 2024-02-09 Hugo Parlier, Dragomir Šarić
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Gradient estimate for solutions of the equation $$\Delta _pv +av^{q}=0$$ on a complete Riemannian manifold Math. Z. (IF 0.8) Pub Date : 2024-02-09
Abstract In this paper, we use the Nash–Moser iteration method to study the local and global behaviors of positive solutions to the nonlinear elliptic equation \(\Delta _pv +av^{q}=0\) defined on a complete Riemannian manifolds (M, g) where \(p>1\) , a and q are constants and \(\Delta _p(v)=\textrm{div}(|\nabla v|^{p-2}\nabla v)\) is the p-Laplace operator. Under some assumptions on a, p and q, we
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Calderón–Zygmund estimates for the fully nonlinear obstacle problem with super-linear Hamiltonian terms and unbounded ingredients Math. Z. (IF 0.8) Pub Date : 2024-02-09 João Vitor da Silva, Romário Tomilhero Frias
In this work, we show the existence/uniqueness of \(L^p\)-viscosity solutions for a fully non-linear obstacle problem with super-linear gradient growth, unbounded ingredients and irregular obstacles. In our results, we obtain Calderón–Zygmund estimates, namely \(W^{2,p}_{loc}\) regularity estimates (with \(p \in \left( \frac{n}{2}, \infty \right) \)) for such solution. Our findings are newsworthy even
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Maximal functions associated to a family of flat curves in lacunary directions Math. Z. (IF 0.8) Pub Date : 2024-02-08
Abstract Consider the maximal operator defined by $$\begin{aligned} \mathcal {M}^{\mathfrak {a}}_{\gamma }f(x_1,x_2)=\sup _{k\in \mathbb {Z}}\sup _{r>0}\frac{1}{2r}\int _{-r}^{r}|f(x_1-t,x_2-a_k\gamma (t))|dt, \end{aligned}$$ where \(\{(t,\gamma (t))\}\) is a convex curve and \(\mathfrak {a}=(a_k)\) is a lacunary sequence. We observe that \(\gamma '\) doubling assumption does not imply to the \(L^p\)
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Revisit on Heisenberg uniqueness pair for the hyperbola Math. Z. (IF 0.8) Pub Date : 2024-02-08 Debkumar Giri, Ramesh Manna
Let \(\Gamma \) be the hyperbola \(\{(x,y)\in \mathbb {R}^2:xy=1\}\) and \(\Lambda _{\alpha , \beta ,\theta _1, \theta _2}\) be the perturbed lattice-cross defined by \(\Lambda _{\alpha , \beta , \theta _1, \theta _2}=\left( (\alpha \mathbb Z+\{\theta _1\})\times \{0\}\right) \cup \left( \{0\}\times (\beta \mathbb Z+\{\theta _2\})\right) \) in \(\mathbb {R}^2\), where \(\theta _1, \theta _2\in \mathbb
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Zeta functions in higher Teichmüller theory Math. Z. (IF 0.8) Pub Date : 2024-02-06 Mark Pollicott, Richard Sharp