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The isomorphism problem for cominuscule Schubert varieties Sel. Math. (IF 1.4) Pub Date : 2024-03-16 Edward Richmond, Mihail Ṭarigradschi, Weihong Xu
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A non-iterative formula for straightening fillings of Young diagrams Sel. Math. (IF 1.4) Pub Date : 2024-03-11 Reuven Hodges
Young diagrams are fundamental combinatorial objects in representation theory and algebraic geometry. Many constructions that rely on these objects depend on variations of a straightening process that expresses a filling of a Young diagram as a sum of semistandard tableaux subject to certain relations. This paper solves the long standing open problem of giving a non-iterative formula for straightening
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When the Fourier transform is one loop exact? Sel. Math. (IF 1.4) Pub Date : 2024-03-09 Maxim Kontsevich, Alexander Odesskii
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Multiplicative structures and random walks in o-minimal groups Sel. Math. (IF 1.4) Pub Date : 2024-03-09 Hunter Spink
We prove structure theorems for o-minimal definable subsets \(S\subset G\) of definable groups containing large multiplicative structures, and show definable groups do not have bounded torsion arbitrarily close to the identity. As an application, for certain models of n-step random walks X in G we show upper bounds \(\mathbb {P}(X\in S)\le n^{-C}\) and a structure theorem for the steps of X when \(\mathbb
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Telescopers for differential forms with one parameter Sel. Math. (IF 1.4) Pub Date : 2024-03-09 Shaoshi Chen, Ruyong Feng, Ziming Li, Michael F. Singer, Stephen M. Watt
Telescopers for a function are linear differential (resp. difference) operators annihilating the definite integral (resp. definite sum) of this function. They play a key role in Wilf–Zeilberger theory and algorithms for computing them have been extensively studied in the past 30 years. In this paper, we introduce the notion of telescopers for differential forms with D-finite function coefficients.
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Whittaker vectors for $$\mathcal {W}$$ -algebras from topological recursion Sel. Math. (IF 1.4) Pub Date : 2024-03-06 Gaëtan Borot, Vincent Bouchard, Nitin K. Chidambaram, Thomas Creutzig
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Knotted toroidal sets, attractors and incompressible surfaces Sel. Math. (IF 1.4) Pub Date : 2024-03-04 Héctor Barge, J. J. Sánchez-Gabites
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The distribution of Weierstrass points on a tropical curve Sel. Math. (IF 1.4) Pub Date : 2024-02-29 David Harry Richman
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The birational geometry of $$\overline{{\mathcal {R}}}_{g,2}$$ and Prym-canonical divisorial strata Sel. Math. (IF 1.4) Pub Date : 2024-02-28
Abstract We prove that the moduli space of double covers ramified at two points \({\mathcal {R}}_{g,2}\) is uniruled for \(3\le g\le 6\) and of general type for \(g\ge 16\) . Furthermore, we consider Prym-canonical divisorial strata in the moduli space \(\overline{{\mathcal {C}}^n{\mathcal {R}}}_g\) parametrizing n-pointed Prym curves, and we compute their classes in \(\textrm{Pic}_{\mathbb {Q}}(\overline{{\mathcal
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The cyclic open–closed map, u-connections and R-matrices Sel. Math. (IF 1.4) Pub Date : 2024-02-27 Kai Hugtenburg
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Galois closures and elementary components of Hilbert schemes of points Sel. Math. (IF 1.4) Pub Date : 2024-02-27 Matthew Satriano, Andrew P. Staal
Bhargava and the first-named author of this paper introduced a functorial Galois closure operation for finite-rank ring extensions, generalizing constructions of Grothendieck and Katz–Mazur. In this paper, we generalize Galois closures and apply them to construct a new infinite family of irreducible components of Hilbert schemes of points. We show that these components are elementary, in the sense
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On the Goncharov depth conjecture and polylogarithms of depth two Sel. Math. (IF 1.4) Pub Date : 2024-02-22 Steven Charlton, Herbert Gangl, Danylo Radchenko, Daniil Rudenko
We prove the surjectivity part of Goncharov’s depth conjecture over a quadratically closed field. We also show that the depth conjecture implies that multiple polylogarithms of depth d and weight n can be expressed via a single function \({{\,\textrm{Li}\,}}_{n-d+1,1,\dots ,1}(a_1,a_2,\dots ,a_d)\), and we prove this latter statement for \(d=2\).
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Davydov–Yetter cohomology and relative homological algebra Sel. Math. (IF 1.4) Pub Date : 2024-02-21 M. Faitg, A. M. Gainutdinov, C. Schweigert
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Monodromy of the equivariant quantum differential equation of the cotangent bundle of a Grassmannian Sel. Math. (IF 1.4) Pub Date : 2024-02-15 Vitaly Tarasov, Alexander Varchenko
We describe the monodromy of the equivariant quantum differential equation of the cotangent bundle of a Grassmannian in terms of the equivariant \(\,K\,\)-theory algebra of the cotangent bundle. This description is based on the hypergeometric integral representations for solutions of the equivariant quantum differential equation. We identify the space of solutions with the space of the equivariant
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Koszul modules with vanishing resonance in algebraic geometry Sel. Math. (IF 1.4) Pub Date : 2024-02-13
Abstract We discuss various applications of a uniform vanishing result for the graded components of the finite length Koszul module associated to a subspace \(K\subseteq \bigwedge ^2 V\) , where V is a vector space. Previously Koszul modules of finite length have been used to give a proof of Green’s Conjecture on syzygies of generic canonical curves. We now give applications to effective stabilization
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Macdonald Duality and the proof of the Quantum Q-system conjecture Sel. Math. (IF 1.4) Pub Date : 2024-02-06
Abstract The \({\textsf{SL}}(2,{{\mathbb {Z}}})\) -symmetry of Cherednik’s spherical double affine Hecke algebras in Macdonald theory includes a distinguished generator which acts as a discrete time evolution of Macdonald operators, which can also be interpreted as a torus Dehn twist in type A. We prove for all twisted and untwisted affine algebras of type ABCD that the time-evolved q-difference Macdonald
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Hall Lie algebras of toric monoid schemes Sel. Math. (IF 1.4) Pub Date : 2024-02-04 Jaiung Jun, Matt Szczesny
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Families of relatively exact Lagrangians, free loop spaces and generalised homology Sel. Math. (IF 1.4) Pub Date : 2024-02-03
Abstract We prove that (under appropriate orientation conditions, depending on R) a Hamiltonian isotopy \(\psi ^1\) of a symplectic manifold \((M, \omega )\) fixing a relatively exact Lagrangian L setwise must act trivially on \(R_*(L)\) , where \(R_*\) is some generalised homology theory. We use a strategy inspired by that of Hu et al. (Geom Topol 15:1617–1650, 2011), who proved an analogous result
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q-Painlevé equations on cluster Poisson varieties via toric geometry Sel. Math. (IF 1.4) Pub Date : 2024-01-27
Abstract We provide a relation between the geometric framework for q-Painlevé equations and cluster Poisson varieties by using toric models of rational surfaces associated with q-Painlevé equations. We introduce the notion of seeds of q-Painlevé type by the negative semi-definiteness of symmetric bilinear forms associated with seeds, and classify the mutation equivalence classes of these seeds. This
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Locally free representations of quivers over commutative Frobenius algebras Sel. Math. (IF 1.4) Pub Date : 2024-01-27 Tamás Hausel, Emmanuel Letellier, Fernando Rodriguez-Villegas
In this paper we investigate locally free representations of a quiver Q over a commutative Frobenius algebra \(\textrm{R}\) by arithmetic Fourier transform. When the base field is finite we prove that the number of isomorphism classes of absolutely indecomposable locally free representations of fixed rank is independent of the orientation of Q. We also prove that the number of isomorphism classes of
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On the local-global principle for isogenies of abelian surfaces Sel. Math. (IF 1.4) Pub Date : 2024-01-26 Davide Lombardo, Matteo Verzobio
Let \(\ell \) be a prime number. We classify the subgroups G of \({\text {Sp}}_4({\mathbb {F}}_\ell )\) and \({\text {GSp}}_4({\mathbb {F}}_\ell )\) that act irreducibly on \({\mathbb {F}}_\ell ^4\), but such that every element of G fixes an \({\mathbb {F}}_\ell \)-vector subspace of dimension 1. We use this classification to prove that a local-global principle for isogenies of degree \(\ell \) between
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Degenerating products of flag varieties and applications to the Breuil–Mézard conjecture Sel. Math. (IF 1.4) Pub Date : 2024-01-19 Robin Bartlett
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Rational endomorphisms of Fano hypersurfaces Sel. Math. (IF 1.4) Pub Date : 2024-01-18 Nathan Chen, David Stapleton
We show that the degrees of rational endomorphisms of very general complex Fano and Calabi–Yau hypersurfaces satisfy certain congruence conditions by specializing to characteristic p. As a corollary we show that very general n-dimensional hypersurfaces of degree \(d\ge \lceil 5(n+3)/6\rceil \) are not birational to Jacobian fibrations of dimension one. A key part of the argument is to resolve singularities
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Generic density of geodesic nets Sel. Math. (IF 1.4) Pub Date : 2024-01-12 Yevgeny Liokumovich, Bruno Staffa
We prove that for a Baire-generic Riemannian metric on a closed smooth manifold, the union of the images of all stationary geodesic nets forms a dense set.
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On rank in algebraic closure Sel. Math. (IF 1.4) Pub Date : 2024-01-13 Amichai Lampert, Tamar Ziegler
Let \( {{\textbf{k}}}\) be a field and \(Q\in {{\textbf{k}}}[x_1, \ldots , x_s]\) a form (homogeneous polynomial) of degree \(d>1.\) The \({{\textbf{k}}}\)-Schmidt rank \(\text {rk}_{{\textbf{k}}}(Q)\) of Q is the minimal r such that \(Q= \sum _{i=1}^r R_iS_i\) with \(R_i, S_i \in {{\textbf{k}}}[x_1, \ldots , x_s]\) forms of degree \(4\). This result has immediate consequences for counting integer
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Spectrum of p-adic linear differential equations I: the shape of the spectrum Sel. Math. (IF 1.4) Pub Date : 2024-01-11 Tinhinane A. Azzouz
This paper extends our previous works Azzouz (Math Z 296(3–4): 1613–1644, 2020; Number Theory 231:139–157, 2022) on determining the spectrum, in the Berkovich sense, of ultrametric linear differential equations. Our previous works focused on equations with constant coefficients or over a field of formal power series. In this paper, we investigate the spectrum of p-adic differential equations at a generic
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Counting orbits of certain infinitely generated non-sharp discontinuous groups for the anti-de Sitter space Sel. Math. (IF 1.4) Pub Date : 2023-12-26 Kazuki Kannaka
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Strongly divisible lattices and crystalline cohomology in the imperfect residue field case Sel. Math. (IF 1.4) Pub Date : 2023-12-27 Yong Suk Moon
Let k be a perfect field of characteristic \(p \ge 3\), and let K be a finite totally ramified extension of \(K_0 = W(k)[p^{-1}]\). Let \(L_0\) be a complete discrete valuation field over \(K_0\) whose residue field has a finite p-basis, and let \(L = L_0\otimes _{K_0} K\). For \(0 \le r \le p-2\), we classify \(\textbf{Z}_p\)-lattices of semistable representations of \(\textrm{Gal}(\overline{L}/L)\)
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The reductive Borel–Serre compactification as a model for unstable algebraic K-theory Sel. Math. (IF 1.4) Pub Date : 2023-12-22 Dustin Clausen, Mikala Ørsnes Jansen
Let A be an associative ring and M a finitely generated projective A-module. We introduce a category \({\text {RBS}}(M)\) and prove several theorems which show that its geometric realisation functions as a well-behaved unstable algebraic K-theory space. These categories \({\text {RBS}}(M)\) naturally arise as generalisations of the exit path \(\infty \)-category of the reductive Borel–Serre compactification
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Vector-relation configurations and plabic graphs Sel. Math. (IF 1.4) Pub Date : 2023-12-21 Niklas Affolter, Max Glick, Pavlo Pylyavskyy, Sanjay Ramassamy
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Formality of differential graded algebras and complex Lagrangian submanifolds Sel. Math. (IF 1.4) Pub Date : 2023-12-15 Borislav Mladenov
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Cohomology of semisimple local systems and the decomposition theorem Sel. Math. (IF 1.4) Pub Date : 2023-12-11 Chuanhao Wei, Ruijie Yang
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Extremality and rigidity for scalar curvature in dimension four Sel. Math. (IF 1.4) Pub Date : 2023-12-14 Renato G. Bettiol, McFeely Jackson Goodman
Following Gromov, a Riemannian manifold is called area-extremal if any modification that increases scalar curvature must decrease the area of some tangent 2-plane. We prove that large classes of compact 4-manifolds, with or without boundary, with nonnegative sectional curvature are area-extremal. We also show that all regions of positive sectional curvature on 4-manifolds are locally area-extremal
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Generators for K-theoretic Hall algebras of quivers with potential Sel. Math. (IF 1.4) Pub Date : 2023-12-08 Tudor Pădurariu
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Partitions, multiple zeta values and the q-bracket Sel. Math. (IF 1.4) Pub Date : 2023-12-07 Henrik Bachmann, Jan-Willem van Ittersum
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Quartic surfaces up to volume preserving equivalence Sel. Math. (IF 1.4) Pub Date : 2023-11-14 Tom Ducat
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Wronskians, total positivity, and real Schubert calculus Sel. Math. (IF 1.4) Pub Date : 2023-11-13 Steven N. Karp
A complete flag in \({\mathbb {R}}^n\) is a sequence of nested subspaces \(V_1 \subset \cdots \subset V_{n-1}\) such that each \(V_k\) has dimension k. It is called totally nonnegative if all its Plücker coordinates are nonnegative. We may view each \(V_k\) as a subspace of polynomials in \({\mathbb {R}}[x]\) of degree at most \(n-1\), by associating a vector \((a_1, \dots , a_n)\) in \({\mathbb {R}}^n\)
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Exact uniform approximation and Dirichlet spectrum in dimension at least two Sel. Math. (IF 1.4) Pub Date : 2023-11-02 Johannes Schleischitz
For \(m\ge 2\), we determine the Dirichlet spectrum in \({\mathbb {R}}^m\) with respect to simultaneous approximation and the maximum norm as the entire interval [0, 1]. This complements previous work of several authors, especially Akhunzhanov and Moshchevitin, who considered \(m=2\) and Euclidean norm. We construct explicit examples of real Liouville vectors realizing any value in the unit interval
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Instanton homology and knot detection on thickened surfaces Sel. Math. (IF 1.4) Pub Date : 2023-10-26 Zhenkun Li, Yi Xie, Boyu Zhang
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Zoo of monotone Lagrangians in $${\mathbb {C}}P^n$$ Sel. Math. (IF 1.4) Pub Date : 2023-10-26 Vardan Oganesyan
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The partial compactification of the universal centralizer Sel. Math. (IF 1.4) Pub Date : 2023-10-27 Ana Bălibanu
The universal centralizer of a semisimple algebraic group G is the family of centralizers of regular elements, parametrized by their conjugacy classes. When G is of adjoint type, we construct a smooth, log-symplectic fiberwise compactification \(\overline{{\mathcal {Z}}}\) of the universal centralizer \({\mathcal {Z}}\) by taking the closure of each fiber in the wonderful compactification \({\overline{G}}\)
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Elliptic Ruijsenaars difference operators, symmetric polynomials, and Wess–Zumino–Witten fusion rings Sel. Math. (IF 1.4) Pub Date : 2023-10-25 Jan Felipe van Diejen, Tamás Görbe
The fusion ring for \(\widehat{\mathfrak {sl}}(n)_m\) Wess–Zumino–Witten conformal field theories is known to be isomorphic to a factor ring of the ring of symmetric polynomials presented by Schur polynomials. We introduce a deformation of this factor ring associated with eigenpolynomials for the elliptic Ruijsenaars difference operators. The corresponding Littlewood–Richardson coefficients are governed
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Homotopy cardinality via extrapolation of Morava–Euler characteristics Sel. Math. (IF 1.4) Pub Date : 2023-10-26 Lior Yanovski
We answer a question of John Baez, on the relationship between the classical Euler characteristic and the Baez–Dolan homotopy cardinality, by constructing a unique additive common generalization after restriction to an odd prime p. This is achieved by \(\ell \)-adically extrapolating to height \(n=-1\) the sequence of Euler characteristics associated with the Morava K(n) cohomology theories for (any)
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Computational aspects of Calogero–Moser spaces Sel. Math. (IF 1.4) Pub Date : 2023-10-24 Cédric Bonnafé, Ulrich Thiel
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t-Structures with Grothendieck hearts via functor categories Sel. Math. (IF 1.4) Pub Date : 2023-10-13 Manuel Saorín, Jan Št’ovíček
We study when the heart of a t-structure in a triangulated category \(\mathcal {D}\) with coproducts is AB5 or a Grothendieck category. If \(\mathcal {D}\) satisfies Brown representability, a t-structure has an AB5 heart with an injective cogenerator and coproduct-preserving associated homological functor if, and only if, the coaisle has a pure-injective t-cogenerating object. If \(\mathcal {D}\) is
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Well ordering principles for iterated $$\Pi ^1_1$$ -comprehension Sel. Math. (IF 1.4) Pub Date : 2023-10-12 Anton Freund, Michael Rathjen
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Le Potier’s strange duality, quot schemes, and multiple point formulas for del Pezzo surfaces Sel. Math. (IF 1.4) Pub Date : 2023-10-10 Aaron Bertram, Thomas Goller, Drew Johnson
We study Le Potier’s strange duality on del Pezzo surfaces using quot schemes to construct independent sections of theta line bundles on moduli spaces of sheaves, one of which is the Hilbert scheme of n points. For \(n \le 7\), we use multiple point formulas to count the length of the quot scheme, which agrees with the dimension of the space of sections on the Hilbert scheme. When the surface is \({\mathbb
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A theorem of Gordan and Noether via Gorenstein rings Sel. Math. (IF 1.4) Pub Date : 2023-10-09 Davide Bricalli, Filippo Francesco Favale, Gian Pietro Pirola
Gordan and Noether proved in their fundamental theorem that an hypersurface \(X=V(F)\subseteq {{\mathbb {P}}}^n\) with \(n\le 3\) is a cone if and only if F has vanishing hessian (i.e. the determinant of the Hessian matrix). They also showed that the statement is false if \(n\ge 4\), by giving some counterexamples. Since their proof, several others have been proposed in the literature. In this paper
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Classification of momentum proper exact Hamiltonian group actions and the equivariant Eliashberg cotangent bundle conjecture Sel. Math. (IF 1.4) Pub Date : 2023-09-27 Fabian Ziltener
Let G be a compact and connected Lie group. The Hamiltonian G-model functor maps the category of symplectic representations of closed subgroups of G to the category of exact Hamiltonian G-actions. Based on previous joint work with Y. Karshon, the restriction of this functor to the momentum proper subcategory on either side induces a bijection between the sets of isomorphism classes. This classifies
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Elliptic stable envelopes and hypertoric loop spaces Sel. Math. (IF 1.4) Pub Date : 2023-09-27 Michael McBreen, Artan Sheshmani, Shing-Tung Yau
This paper describes a relation between the elliptic stable envelopes of a hypertoric variety \(X\) and a distinguished K-theory class on the product of the loop hypertoric space \(\widetilde{\mathscr {L}}X\) and its symplectic dual \(\mathscr {P}X^!\). This class intertwines the K-theoretic stable envelopes in a certain limit. Our results are suggestive of a possible categorification of elliptic stable
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Equivariant pliability of the projective space Sel. Math. (IF 1.4) Pub Date : 2023-09-21 Ivan Cheltsov, Arman Sarikyan
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Holonomic functions and prehomogeneous spaces Sel. Math. (IF 1.4) Pub Date : 2023-09-19 András Cristian Lőrincz
A function that is analytic on a domain of \({\mathbb {C}}^n\) is holonomic if it is the solution to a holonomic system of linear homogeneous differential equations with polynomial coefficients. We define and study the Bernstein–Sato polynomial of a holonomic function on a smooth algebraic variety. We analyze the structure of certain sheaves of holonomic functions, such as the algebraic functions along
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Thickening of the diagonal and interleaving distance Sel. Math. (IF 1.4) Pub Date : 2023-09-20 François Petit, Pierre Schapira
Given a topological space X, a thickening kernel is a monoidal presheaf on \(({{\mathbb {R}}}_{\ge 0},+)\) with values in the monoidal category of derived kernels on X. A bi-thickening kernel is defined on \(({{\mathbb {R}}},+)\). To such a thickening kernel, one naturally associates an interleaving distance on the derived category of sheaves on X. We prove that a thickening kernel exists and is unique
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Whitney stratifications are conically smooth Sel. Math. (IF 1.4) Pub Date : 2023-09-15 Guglielmo Nocera, Marco Volpe
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Entropy collapse versus entropy rigidity for Reeb and Finsler flows Sel. Math. (IF 1.4) Pub Date : 2023-08-31 Alberto Abbondandolo, Marcelo R. R. Alves, Murat Sağlam, Felix Schlenk
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Quantum parameters of the geometric Langlands theory Sel. Math. (IF 1.4) Pub Date : 2023-08-22 Yifei Zhao
Fix a smooth, complete algebraic curve X over an algebraically closed field k of characteristic zero. To a reductive group G over k, we associate an algebraic stack \({\text {Par}}_G\) of quantum parameters for the geometric Langlands theory. Then we construct a family of (quasi-)twistings parametrized by \({\text {Par}}_G\), whose module categories give rise to twisted \({\mathcal {D}}\)-modules on
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On Gromov–Yomdin type theorems and a categorical interpretation of holomorphicity Sel. Math. (IF 1.4) Pub Date : 2023-08-21 Federico Barbacovi, Jongmyeong Kim
In topological dynamics, the Gromov–Yomdin theorem states that the topological entropy of a holomorphic automorphism f of a smooth projective variety is equal to the logarithm of the spectral radius of the induced map \(f^*\). In order to establish a categorical analogue of the Gromov–Yomdin theorem, one first needs to find a categorical analogue of a holomorphic automorphism. In this paper, we propose