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  • Laurent phenomenon algebras arising from surfaces II: Laminated surfaces
    Sel. Math. (IF 1.053) Pub Date : 2020-10-14
    Jon Wilson

    It was shown by Fock and Goncharov (Dual Teichmüller and lamination spaces. Handbook of Teichmüller Theory, 2007), and Fomin et al. (Acta Math 201(1):83–146, 2008) that some cluster algebras arise from triangulated orientable surfaces. Subsequently, Dupont and Palesi (J Algebraic Combinatorics 42(2):429–472, 2015) generalised this construction to include unpunctured non-orientable surfaces, giving

    更新日期:2020-10-14
  • Connectivity of joins, cohomological quantifier elimination, and an algebraic Toda’s theorem
    Sel. Math. (IF 1.053) Pub Date : 2020-10-11
    Saugata Basu, Deepam Patel

    In this article, we use cohomological techniques to obtain an algebraic version of Toda’s theorem in complexity theory valid over algebraically closed fields of arbitrary characteristic. This result follows from a general ‘connectivity’ result in cohomology. More precisely, given a closed subvariety \(X \subset {\mathbb {P}}^{n}\) over an algebraically closed field k, and denoting by \(\mathrm{J}^{[p]}(X)

    更新日期:2020-10-11
  • Bott–Samelson atlases, total positivity, and Poisson structures on some homogeneous spaces
    Sel. Math. (IF 1.053) Pub Date : 2020-10-10
    Jiang-Hua Lu, Shizhuo Yu

    Let G be a connected and simply connected complex semisimple Lie group. For a collection of homogeneous G-spaces G/Q, we construct a finite atlas \({{\mathcal {A}}}_{{\scriptscriptstyle BS}}(G/Q)\) on G/Q, called the Bott–Samelson atlas, and we prove that all of its coordinate functions are positive with respect to the Lusztig positive structure on G/Q. We also show that the standard Poisson structure

    更新日期:2020-10-11
  • The persistence of the Chekanov–Eliashberg algebra
    Sel. Math. (IF 1.053) Pub Date : 2020-10-09
    Georgios Dimitroglou Rizell, Michael G. Sullivan

    We apply the barcodes of persistent homology theory to the c Chekanov–Eliashberg algebra of a Legendrian submanifold to deduce displacement energy bounds for arbitrary Legendrians. We do not require the full Chekanov–Eliashberg algebra to admit an augmentation as we linearize the algebra only below a certain action level. As an application we show that it is not possible to \(C^0\)-approximate a stabilized

    更新日期:2020-10-11
  • Ekeland’s variational principle in weak and strong systems of arithmetic
    Sel. Math. (IF 1.053) Pub Date : 2020-10-02
    David Fernández-Duque, Paul Shafer, Keita Yokoyama

    We analyze Ekeland’s variational principle in the context of reverse mathematics. We find that that the full variational principle is equivalent to \(\Pi ^1_1\text{- }\mathsf {CA}_0\), a strong theory of second-order arithmetic, while natural restrictions (e.g. to compact spaces or to continuous functions) yield statements equivalent to weak König’s lemma (\(\mathsf {WKL}_0\)) and to arithmetical comprehension

    更新日期:2020-10-04
  • Canonical lifts and $$\delta $$ δ -structures
    Sel. Math. (IF 1.053) Pub Date : 2020-09-30
    James Borger, Lance Gurney

    We extend the Serre–Tate theory of canonical lifts of ordinary abelian varieties to arbitrary unpolarised families of ordinary abelian varieties parameterised by a p-adic formal scheme S. We show that the canonical lift is the unique lift to W(S) which admits a \(\delta \)-structure in the sense of Joyal, Buium, and Bousfield. We prove analogous statements for families of ordinary p-groups and p-divisible

    更新日期:2020-09-30
  • Generic differential operators on Siegel modular forms and special polynomials
    Sel. Math. (IF 1.053) Pub Date : 2020-09-28
    Tomoyoshi Ibukiyama

    Holomorphic vector valued differential operators acting on Siegel modular forms and preserving automorphy under the restriction to diagonal blocks are important in many respects, including application to critical values of L functions. Such differential operators are associated with vectors of new special polynomials of several variables defined by certain harmonic conditions. They include the classical

    更新日期:2020-09-28
  • Sub-leading asymptotics of ECH capacities
    Sel. Math. (IF 1.053) Pub Date : 2020-09-24
    Dan Cristofaro-Gardiner, Nikhil Savale

    In previous work (Cristofaro-Gardiner et al. in Invent Math 199:187–214, 2015), the first author and collaborators showed that the leading asymptotics of the embedded contact homology spectrum recovers the contact volume. Our main theorem here is a new bound on the sub-leading asymptotics.

    更新日期:2020-09-24
  • On maximal proper subgroups of field automorphism groups
    Sel. Math. (IF 1.053) Pub Date : 2006
    M. Rovinsky

    Let G be the automorphism group of an extension \(F\mid k\) of algebraically closed fields of characteristic zero of transcendence degree n, 1 ≤ n ≤ ∞. In this paper we construct some maximal closed non-open subgroups G v , and some (all, in the case of countable transcendence degree) maximal open proper subgroups of G; describe, in the case of countable transcendence degree, the automorphism subgroups

    更新日期:2020-09-24
  • Hall-type algebras for categorical Donaldson–Thomas theories on local surfaces
    Sel. Math. (IF 1.053) Pub Date : 2020-09-14
    Yukinobu Toda

    We show that the categorified cohomological Hall algebra structures on surfaces constructed by Porta–Sala descend to those on Donaldson–Thomas categories on local surfaces introduced in the author’s previous paper. A similar argument also shows that Pandharipande–Thomas categories on local surfaces admit actions of categorified COHA for zero dimensional sheaves on surfaces. We also construct annihilator

    更新日期:2020-09-14
  • Large values of cusp forms on $$\mathrm {GL}_n$$ GL n
    Sel. Math. (IF 1.053) Pub Date : 2020-09-09
    Farrell Brumley; Nicolas Templier

    We establish the transition behavior of Jacquet–Whittaker functions on split semi-simple Lie groups. As a consequence, we show that for certain finite volume Riemannian manifolds, the local bound for normalized Laplace eigenfunctions does not hold globally.

    更新日期:2020-09-09
  • Generators, spanning sets and existence of twisted modules for a grading-restricted vertex (super)algebra
    Sel. Math. (IF 1.053) Pub Date : 2020-09-08
    Yi-Zhi Huang

    For a grading-restricted vertex superalgebra V and an automorphism g of V, we give a linearly independent set of generators of the universal lower-bounded generalized g-twisted V-module \({\widehat{M}}^{[g]}_{B}\) constructed by the author in Huang (Commun Math Phys 377:909–945 (2020)). We prove that there exist irreducible lower-bounded generalized g-twisted V-modules by showing that there exists

    更新日期:2020-09-08
  • Constructing smooth and fully faithful tropicalizations for Mumford curves
    Sel. Math. (IF 1.053) Pub Date : 2020-08-10
    Philipp Jell

    The tropicalization of an algebraic variety X is a combinatorial shadow of X, which is sensitive to a closed embedding of X into a toric variety. Given a good embedding, the tropicalization can provide a lot of information about X. We construct two types of these good embeddings for Mumford curves: fully faithful tropicalizations, which are embeddings such that the tropicalization admits a continuous

    更新日期:2020-08-10
  • Unramified affine Springer fibers and isospectral Hilbert schemes
    Sel. Math. (IF 1.053) Pub Date : 2020-08-10
    Oscar Kivinen

    For any connected reductive group G over \({{\mathbb {C}}}\), we revisit Goresky–Kottwitz–MacPherson’s description of the torus equivariant Borel–Moore homology of affine Springer fibers \({\mathrm {Sp}}_{\gamma }\subset {{\,\mathrm{Gr}\,}}_G\), where \(\gamma =zt^d\) and z is a regular semisimple element in the Lie algebra of G. In the case \(G=GL_n\), we relate the equivariant cohomology of \({\mathrm

    更新日期:2020-08-10
  • Reflexive polytopes arising from bipartite graphs with $$\gamma $$ γ -positivity associated to interior polynomials
    Sel. Math. (IF 1.053) Pub Date : 2020-08-10
    Hidefumi Ohsugi; Akiyoshi Tsuchiya

    In this paper, we introduce polytopes \({\mathscr {B}}_G\) arising from root systems \(B_n\) and finite graphs G, and study their combinatorial and algebraic properties. In particular, it is shown that \({\mathscr {B}}_G\) is reflexive if and only if G is bipartite. Moreover, in the case, \({\mathscr {B}}_G\) has a regular unimodular triangulation. This implies that the \(h^*\)-polynomial of \({\mathscr

    更新日期:2020-08-10
  • The Haydys monopole equation
    Sel. Math. (IF 1.053) Pub Date : 2020-08-08
    Ákos Nagy; Gonçalo Oliveira

    We study complexified Bogomolny monopoles using the complex linear extension of the Hodge star operator, these monopoles can be interpreted as solutions to the Bogomolny equation with a complex gauge group. Alternatively, these equations can be obtained from dimensional reduction of the Haydys instanton equations to three dimensions, thus we call them Haydys monopoles. We find that (under mild hypotheses)

    更新日期:2020-08-08
  • Donaldson–Thomas invariants from tropical disks
    Sel. Math. (IF 1.053) Pub Date : 2020-07-28
    Man-Wai Cheung; Travis Mandel

    We prove that the quantum DT-invariants associated to quivers with genteel potential can be expressed in terms of certain refined counts of tropical disks. This is based on a quantum version of Bridgeland’s description of cluster scattering diagrams in terms of stability conditions, plus a new version of the description of scattering diagrams in terms of tropical disk counts. The weights with which

    更新日期:2020-07-28
  • Some upper bounds on ordinal-valued Ramsey numbers for colourings of pairs
    Sel. Math. (IF 1.053) Pub Date : 2020-07-21
    Leszek Aleksander Kołodziejczyk; Keita Yokoyama

    We study Ramsey’s theorem for pairs and two colours in the context of the theory of \(\alpha \)-large sets introduced by Ketonen and Solovay. We prove that any 2-colouring of pairs from an \(\omega ^{300n}\)-large set admits an \(\omega ^n\)-large homogeneous set. We explain how a formalized version of this bound gives a more direct proof, and a strengthening, of the recent result of Patey and Yokoyama

    更新日期:2020-07-21
  • Concomitants of ternary quartics and vector-valued Siegel and Teichmüller modular forms of genus three
    Sel. Math. (IF 1.053) Pub Date : 2020-07-20
    Fabien Cléry; Carel Faber; Gerard van der Geer

    We show how one can use the representation theory of ternary quartics to construct all vector-valued Siegel modular forms and Teichmüller modular forms of degree 3. The relation between the order of vanishing of a concomitant on the locus of double conics and the order of vanishing of the corresponding modular form on the hyperelliptic locus plays an important role. We also determine the connection

    更新日期:2020-07-20
  • Maximal estimates for the Schrödinger equation with orthonormal initial data
    Sel. Math. (IF 1.053) Pub Date : 2020-07-20
    Neal Bez; Sanghyuk Lee; Shohei Nakamura

    For the one-dimensional Schrödinger equation, we obtain sharp maximal-in-time and maximal-in-space estimates for systems of orthonormal initial data. The maximal-in-time estimates generalize a classical result of Kenig–Ponce–Vega and allow us to obtain pointwise convergence results associated with systems of infinitely many fermions. The maximal-in-space estimates simultaneously address an endpoint

    更新日期:2020-07-20
  • A hardness of approximation result in metric geometry
    Sel. Math. (IF 1.053) Pub Date : 2020-07-20
    Zarathustra Brady; Larry Guth; Fedor Manin

    We show that it is \({\mathsf {NP}}\)-hard to approximate the hyperspherical radius of a triangulated manifold up to an almost-polynomial factor.

    更新日期:2020-07-20
  • Order antimorphisms of finite-dimensional cones
    Sel. Math. (IF 1.053) Pub Date : 2020-07-20
    Cormac Walsh

    We show that an order antimorphism on a finite-dimensional cone having no one-dimensional factors is homogeneous of degree \(-\,1\). A consequence is that the only finite-dimensional cones admitting an order antimorphism are the symmetric cones.

    更新日期:2020-07-20
  • Categorical Bernstein operators and the Boson-Fermion correspondence
    Sel. Math. (IF 1.053) Pub Date : 2020-07-13
    Nicolle S. González

    We prove a conjecture of Cautis and Sussan providing a categorification of the Boson-Fermion correspondence as formulated by Frenkel and Kac. We lift the Bernstein operators to infinite chain complexes in Khovanov’s Heisenberg category \({\mathcal {H}}\) and from them construct categorical analogues of the Kac-Frenkel fermionic vertex operators. These fermionic functors are then shown to satisfy categorical

    更新日期:2020-07-13
  • Computation of cohomology of Lie conformal and Poisson vertex algebras
    Sel. Math. (IF 1.053) Pub Date : 2020-07-10
    Bojko Bakalov; Alberto De Sole; Victor G. Kac

    We develop methods for computation of Poisson vertex algebra cohomology. This cohomology is computed for the free bosonic and fermionic Poisson vertex (super)algebras, as well as for the universal affine and Virasoro Poisson vertex algebras. We establish finite dimensionality of this cohomology for conformal Poisson vertex (super)algebras that are finitely and freely generated by elements of positive

    更新日期:2020-07-10
  • The de Rham functor for logarithmic D-modules
    Sel. Math. (IF 1.053) Pub Date : 2020-07-06
    Clemens Koppensteiner

    In the first part we deepen the six-functor theory of (holonomic) logarithmic D-modules, in particular with respect to duality and pushforward along projective morphisms. Then, inspired by work of Ogus, we define a logarithmic analogue of the de Rham functor, sending logarithmic D-modules to certain graded sheaves on the so-called Kato–Nakayama space. For holonomic modules we show that the associated

    更新日期:2020-07-06
  • Deformation theory of the blown-up Seiberg–Witten equation in dimension three
    Sel. Math. (IF 1.053) Pub Date : 2020-07-06
    Aleksander Doan; Thomas Walpuski

    Associated with every quaternionic representation of a compact, connected Lie group there is a Seiberg–Witten equation in dimension three. The moduli spaces of solutions to these equations are typically non-compact. We construct Kuranishi models around boundary points of a partially compactified moduli space. The Haydys correspondence identifies such boundary points with Fueter sections—solutions of

    更新日期:2020-07-06
  • Discrete and continuous symmetries in monotone Floer theory
    Sel. Math. (IF 1.053) Pub Date : 2020-06-29
    Jack Smith

    This paper studies the self-Floer theory of a monotone Lagrangian submanifold L of a symplectic manifold X in the presence of various kinds of symmetry. First we suppose L is K-homogeneous and compute the image of low codimension K-invariant subvarieties of X under the length-zero closed–open string map. Next we consider the group \(\mathrm {Symp}(X, L)\) of symplectomorphisms of X preserving L setwise

    更新日期:2020-06-29
  • Torsion pairs for quivers and the Weyl groups
    Sel. Math. (IF 1.053) Pub Date : 2020-06-29
    Yuya Mizuno; Hugh Thomas

    We give an interpretation of the map \(\pi ^c\) defined by Reading, which is a map from the elements of a Coxeter group to the c-sortable elements, in terms of the representation theory of preprojective algebras. Moreover, we study a close relationship between c-sortable elements and torsion pairs, and give an explicit description of the cofinite torsion classes in the context of the Coxeter group

    更新日期:2020-06-29
  • Parameterization of factorizable line bundles by K -theory and motivic cohomology
    Sel. Math. (IF 1.053) Pub Date : 2020-06-22
    Dennis Gaitsgory

    In this note we show how to construct a factorizable line bundle on the affine Grassmannian of a group G starting from a Brylinski-Deligne datum, which is an extension of G by the Zaraski-sheafified \(K_2\).

    更新日期:2020-06-22
  • Non-commutative deformations of simple objects in a category of perverse coherent sheaves
    Sel. Math. (IF 1.053) Pub Date : 2020-06-22
    Yujiro Kawamata

    We define a category of perverse coherent sheaves as the abelian category corresponding to the category of modules under Bondal–Rickard equivalence which arises from a tilting bundle for a projective morphism. The purpose of this paper is to determine versal non-commutative deformations of simple collections in the categories of perverse coherent sheaves in some cases. In general we prove that the

    更新日期:2020-06-22
  • The monodromy groups of lisse sheaves and overconvergent F -isocrystals
    Sel. Math. (IF 1.053) Pub Date : 2020-06-22
    Marco D’Addezio

    It has been proven by Serre, Larsen–Pink and Chin, that over a smooth curve over a finite field, the monodromy groups of compatible semi-simple pure lisse sheaves have “the same” \(\pi _0\) and neutral component. We generalize their results to compatible systems of semi-simple lisse sheaves and overconvergent F-isocrystals over arbitrary smooth varieties. For this purpose, we extend the theorem of

    更新日期:2020-06-22
  • Uniform description of the rigged configuration bijection
    Sel. Math. (IF 1.053) Pub Date : 2020-06-17
    Travis Scrimshaw

    We give a uniform description of the bijection \(\Phi \) from rigged configurations to tensor products of Kirillov–Reshetikhin crystals of the form \(\bigotimes _{i=1}^N B^{r_i,1}\) in dual untwisted types: simply-laced types and types \(A_{2n-1}^{(2)}\), \(D_{n+1}^{(2)}\), \(E_6^{(2)}\), and \(D_4^{(3)}\). We give a uniform proof that \(\Phi \) is a bijection and preserves statistics. We describe

    更新日期:2020-06-17
  • Schur rigidity of Schubert varieties in rational homogeneous manifolds of Picard number one
    Sel. Math. (IF 1.053) Pub Date : 2020-06-15
    Jaehyun Hong; Ngaiming Mok

    Given a rational homogeneous manifold \(S=G/P\) of Picard number one and a Schubert variety \(S_0 \) of S, the pair \((S,S_0)\) is said to be homologically rigid if any subvariety of S having the same homology class as \(S_0\) must be a translate of \(S_0\) by the automorphism group of S. The pair \((S,S_0)\) is said to be Schur rigid if any subvariety of S with homology class equal to a multiple of

    更新日期:2020-06-15
  • q -Deformed character theory for infinite-dimensional symplectic and orthogonal groups
    Sel. Math. (IF 1.053) Pub Date : 2020-06-12
    Cesar Cuenca; Vadim Gorin

    The classification of irreducible, spherical characters of the infinite-dimensional unitary/orthogonal/symplectic groups can be obtained by finding all possible limits of normalized, irreducible characters of the corresponding finite-dimensional groups, as the rank tends to infinity. We solve a q-deformed version of the latter problem for orthogonal and symplectic groups, extending previously known

    更新日期:2020-06-12
  • Derived equivalence and Grothendieck ring of varieties: the case of K3 surfaces of degree 12 and abelian varieties
    Sel. Math. (IF 1.053) Pub Date : 2020-06-11
    Atsushi Ito; Makoto Miura; Shinnosuke Okawa; Kazushi Ueda

    In this paper, we discuss the problem of whether the difference \([X]-[Y]\) of the classes of a Fourier–Mukai pair (X, Y) of smooth projective varieties in the Grothendieck ring of varieties is annihilated by some power of the class \(\mathbb {L} = [ \mathbb {A}^1 ]\) of the affine line. We give an affirmative answer for Fourier–Mukai pairs of very general K3 surfaces of degree 12. On the other hand

    更新日期:2020-06-11
  • Remarks on K (1)-local K -theory
    Sel. Math. (IF 1.053) Pub Date : 2020-06-11
    Bhargav Bhatt; Dustin Clausen; Akhil Mathew

    We prove two basic structural properties of the algebraic K-theory of rings after K(1)-localization at an implicit prime p. Our first result (also recently obtained by Land–Meier–Tamme by different methods) states that \(L_{K(1)} K(R)\) is insensitive to inverting p on R; we deduce this from recent advances in prismatic cohomology and \(\mathrm {TC}\). Our second result yields a Künneth formula in

    更新日期:2020-06-11
  • Special Kähler structures, cubic differentials and hyperbolic metrics
    Sel. Math. (IF 1.053) Pub Date : 2020-06-11
    Andriy Haydys; Bin Xu

    We obtain necessary conditions for the existence of special Kähler structures with isolated singularities on compact Riemann surfaces. We prove that these conditions are also sufficient in the case of the Riemann sphere and, moreover, we determine the whole moduli space of special Kähler structures with fixed singularities. The tool we develop for this aim is a correspondence between special Kähler

    更新日期:2020-06-11
  • On symmetric fusion categories in positive characteristic
    Sel. Math. (IF 1.053) Pub Date : 2020-06-09
    Victor Ostrik

    We propose a conjectural extension in the positive characteristic case of well known Deligne’s theorem on the existence of super fiber functors. We prove our conjecture in the special case of semisimple categories with finitely many isomorphism classes of simple objects.

    更新日期:2020-06-09
  • Topological and geometric aspects of almost Kähler manifolds via harmonic theory
    Sel. Math. (IF 1.053) Pub Date : 2020-06-09
    Joana Cirici; Scott O. Wilson

    The well-known Kähler identities naturally extend to the non-integrable setting. This paper deduces several geometric and topological consequences of these extended identities for compact almost Kähler manifolds. Among these are identities of various Laplacians, generalized Hodge and Serre dualities, a generalized hard Lefschetz duality, and a Lefschetz decomposition, all on the space of d-harmonic

    更新日期:2020-06-09
  • Polynomial graph invariants and the KP hierarchy
    Sel. Math. (IF 1.053) Pub Date : 2020-06-08
    Sergei Chmutov; Maxim Kazarian; Sergei Lando

    We prove that the generating function for the symmetric chromatic polynomial of all simple graphs is (after an appropriate scaling change of variables) a linear combination of one-part Schur polynomials. This statement immediately implies that it is also a \(\tau \)-function of the Kadomtsev–Petviashvili integrable hierarchy of mathematical physics. Moreover, we describe a large family of polynomial

    更新日期:2020-06-08
  • The realization problem for finitely generated refinement monoids
    Sel. Math. (IF 1.053) Pub Date : 2020-05-20
    Pere Ara; Joan Bosa; Enrique Pardo

    We show that every finitely generated conical refinement monoid can be represented as the monoid \(\mathcal V (R)\) of isomorphism classes of finitely generated projective modules over a von Neumann regular ring R. To this end, we use the representation of these monoids provided by adaptable separated graphs. Given an adaptable separated graph (E, C) and a field K, we build a von Neumann regular K-algebra

    更新日期:2020-05-20
  • An Alexander polynomial for MOY graphs
    Sel. Math. (IF 1.053) Pub Date : 2020-04-18
    Yuanyuan Bao; Zhongtao Wu

    We introduce an Alexander polynomial for MOY graphs. For a framed trivalent MOY graph \({\mathbb {G}}\), we refine the construction and obtain a framed ambient isotopy invariant \(\Delta _{({\mathbb {G}},c)}(t)\). The invariant \(\Delta _{({\mathbb {G}}, c)}(t)\) satisfies a series of relations, which we call MOY-type relations, and conversely these relations determine \(\Delta _{({\mathbb {G}}, c)}(t)\)

    更新日期:2020-04-18
  • On the indivisibility of derived Kato’s Euler systems and the main conjecture for modular forms
    Sel. Math. (IF 1.053) Pub Date : 2020-04-16
    Chan-Ho Kim; Myoungil Kim; Hae-Sang Sun

    We provide a simple and efficient numerical criterion to verify the Iwasawa main conjecture and the indivisibility of derived Kato’s Euler systems for modular forms of weight two at any good prime under mild assumptions. In the ordinary case, the criterion works for all members of a Hida family once and for all. The key ingredient is the explicit computation of the integral image of the derived Kato’s

    更新日期:2020-04-16
  • Cohomological Hall algebras for Higgs torsion sheaves, moduli of triples and sheaves on surfaces
    Sel. Math. (IF 1.053) Pub Date : 2020-04-15
    Alexandre Minets

    For any free oriented Borel–Moore homology theory A, we construct an associative product on the A-theory of the stack of Higgs torsion sheaves over a projective curve C. We show that the resulting algebra \(A\mathbf{Ha}_C^0\) admits a natural shuffle presentation, and prove it is faithful when A is replaced with usual Borel–Moore homology groups. We also introduce moduli spaces of stable triples, heavily

    更新日期:2020-04-15
  • Euler characteristics in the quantum K -theory of flag varieties
    Sel. Math. (IF 1.053) Pub Date : 2020-04-10
    Anders S. Buch; Sjuvon Chung; Changzheng Li; Leonardo C. Mihalcea

    We prove that the sheaf Euler characteristic of the product of a Schubert class and an opposite Schubert class in the quantum K-theory ring of a (generalized) flag variety G/P is equal to \(q^d\), where d is the smallest degree of a rational curve joining the two Schubert varieties. This implies that the sum of the structure constants of any product of Schubert classes is equal to 1. Along the way

    更新日期:2020-04-10
  • The ABC of p-cells
    Sel. Math. (IF 1.053) Pub Date : 2020-04-08
    Lars Thorge Jensen

    Parallel to the very rich theory of Kazhdan–Lusztig cells in characteristic 0, we try to build a similar theory in positive characteristic. We study cells with respect to the p-canonical basis of the Hecke algebra of a crystallographic Coxeter system (see Jensen and Williamson in Categorification and higher representation theory, American Mathematical Society, Providence, 2017). Our main technical

    更新日期:2020-04-08
  • Momentum polytopes of projective spherical varieties and related Kähler geometry
    Sel. Math. (IF 1.053) Pub Date : 2020-04-06
    Stéphanie Cupit-Foutou; Guido Pezzini; Bart Van Steirteghem

    We apply the combinatorial theory of spherical varieties to characterize the momentum polytopes of polarized projective spherical varieties. This enables us to derive a classification of these varieties, without specifying the open orbit, as well as a classification of all Fano spherical varieties. In the setting of multiplicity free compact and connected Hamiltonian manifolds, we obtain a necessary

    更新日期:2020-04-06
  • Lagrangian skeleta of hypersurfaces in $$({\mathbb {C}}^*)^n$$(C∗)n
    Sel. Math. (IF 1.053) Pub Date : 2020-03-30
    Peng Zhou

    Let \(W(z_1, \ldots , z_n): ({\mathbb {C}}^*)^n \rightarrow {\mathbb {C}}\) be a Laurent polynomial in n variables, and let \({\mathcal {H}}\) be a generic smooth fiber of W. Ruddat et al. (Geom Topol 18:1343–1395, 2014) give a combinatorial recipe for a skeleton for \({\mathcal {H}}\). In this paper, we show that for a suitable exact symplectic structure on \({\mathcal {H}}\), the RSTZ-skeleton can

    更新日期:2020-03-30
  • Cutting lemma and Zarankiewicz’s problem in distal structures
    Sel. Math. (IF 1.053) Pub Date : 2020-03-16
    Artem Chernikov; David Galvin; Sergei Starchenko

    We establish a cutting lemma for definable families of sets in distal structures, as well as the optimality of the distal cell decomposition for definable families of sets on the plane in o-minimal expansions of fields. Using it, we generalize the results in Fox et al. (J Eur Math Soc 19(6):1785–1810, 2017 ) on the semialgebraic planar Zarankiewicz problem to arbitrary o-minimal structures, in particular

    更新日期:2020-03-16
  • Classifying fusion categories $$\otimes $$⊗ -generated by an object of small Frobenius–Perron dimension
    Sel. Math. (IF 1.053) Pub Date : 2020-03-13
    Cain Edie-Michell

    The goal of this paper is to classify fusion categories \({\mathcal {C}}\) which are \(\otimes \)-generated by an object X of Frobenius–Perron dimension less than 2, with the additional mild assumption that the adjoint subcategory of \({\mathcal {C}}\) is \(\otimes \)-generated by the object \(X\otimes X^*\). This classification has recently become accessible due to a result of Morrison and Snyder

    更新日期:2020-03-13
  • Singular compactness and definability for $$\Sigma $$Σ -cotorsion and Gorenstein modules
    Sel. Math. (IF 1.053) Pub Date : 2020-03-12
    Jan Šaroch; Jan Št’ovíček

    We introduce a general version of the singular compactness theorem which makes it possible to show that being a \(\Sigma \)-cotorsion module is a property of the complete theory of the module. As an application of the powerful tools developed along the way, we give a new description of Gorenstein flat modules which implies that, regardless of the ring, the class of all Gorenstein flat modules forms

    更新日期:2020-03-12
  • Bivariate polynomial injections and elliptic curves
    Sel. Math. (IF 1.053) Pub Date : 2020-03-07
    Hector Pasten

    For every number field k, we construct an affine algebraic surface X over k with a Zariski dense set of k-rational points, and a regular function f on X inducing an injective map \(X(k)\rightarrow k\) on k-rational points. In fact, given any elliptic curve E of positive rank over k, we can take \(X=V\times V\) with V a suitable affine open set of E. The method of proof combines value distribution theory

    更新日期:2020-03-07
  • The affine VW supercategory
    Sel. Math. (IF 1.053) Pub Date : 2020-03-07
    M. Balagović; Z. Daugherty; I. Entova-Aizenbud; I. Halacheva; J. Hennig; M. S. Im; G. Letzter; E. Norton; V. Serganova; C. Stroppel

    We define the affine VW supercategory , which arises from studying the action of the periplectic Lie superalgebra \(\mathfrak {p}(n)\) on the tensor product \(M\otimes V^{\otimes a}\) of an arbitrary representation M with several copies of the vector representation V of \(\mathfrak {p}(n)\). It plays a role analogous to that of the degenerate affine Hecke algebras in the context of representations

    更新日期:2020-03-07
  • Nearby cycles of parahoric shtukas, and a fundamental lemma for base change
    Sel. Math. (IF 1.053) Pub Date : 2020-03-07
    Tony Feng

    Using the Langlands–Kottwitz paradigm, we compute the trace of Frobenius composed with Hecke operators on the cohomology of nearby cycles, at places of parahoric reduction, of perverse sheaves on certain moduli stacks of shtukas. Following an argument of Ngô, we then use this to give a geometric proof of a base change fundamental lemma for parahoric Hecke algebras for \({\text {GL}}_n\) over local

    更新日期:2020-03-07
  • Holonomy braidings, biquandles and quantum invariants of links with $$\mathsf {SL} _2(\mathbb {C} )$$SL2(C) flat connections
    Sel. Math. (IF 1.053) Pub Date : 2020-03-03
    Christian Blanchet; Nathan Geer; Bertrand Patureau-Mirand; Nicolai Reshetikhin

    R. Kashaev and N. Reshetikhin introduced the notion of holonomy braiding extending V. Turaev’s homotopy braiding to describe the behavior of cyclic representations of the unrestricted quantum group \({U_q{\mathfrak {sl}(2)}}\) at root of unity. In this paper, using quandles and biquandles we develop a general theory for Reshetikhin–Turaev ribbon type functor for tangles with quandle representations

    更新日期:2020-03-03
  • Indefinite Stein fillings and $$\text {PIN}(2)$$PIN(2) -monopole Floer homology
    Sel. Math. (IF 1.053) Pub Date : 2020-02-29
    Francesco Lin

    We introduce techniques to study the topology of Stein fillings of a given contact three-manifold \((Y,\xi )\) which are not negative definite. For example, given a \(\hbox {spin}^c\) rational homology sphere \((Y,{\mathfrak {s}})\) with \({\mathfrak {s}}\) self-conjugate such that the reduced monopole Floer homology group \({\textit{HM}}_{\bullet }(Y,{\mathfrak {s}})\) has dimension one, we show that

    更新日期:2020-02-29
  • Braid group symmetries of Grassmannian cluster algebras
    Sel. Math. (IF 1.053) Pub Date : 2020-02-20
    Chris Fraser

    Let \({{\,\mathrm{\text{ Gr }}\,}}^\circ (k,n) \subset {{\,\mathrm{\text{ Gr }}\,}}(k,n)\) denote the open positroid stratum in the Grassmannian. We define an action of the extended affine d-strand braid group on \({{\,\mathrm{\text{ Gr }}\,}}^\circ (k,n)\) by regular automorphisms, for d the greatest common divisor of k and n. The action is by quasi-automorphisms of the cluster structure on \({{\

    更新日期:2020-02-20
  • Tropicalizing the moduli space of spin curves
    Sel. Math. (IF 1.053) Pub Date : 2020-02-18
    Lucia Caporaso; Margarida Melo; Marco Pacini

    We study the tropicalization of the moduli space of algebraic spin curves, \(\overline{\mathcal {S}}_{g,n}\). We exhibit its combinatorial stratification and prove that the strata are irreducible. We construct the moduli space of tropical spin curves \(\overline{S}_{g,n}^{{\text {trop}}}\), prove that is naturally isomorphic to the skeleton of the analytification, \(\overline{S}_{g,n}^{{\text {an}}}\)

    更新日期:2020-02-18
  • Flip cycles in plabic graphs
    Sel. Math. (IF 1.053) Pub Date : 2020-02-17
    Alexey Balitskiy; Julian Wellman

    Planar bicolored (plabic) graphs are combinatorial objects introduced by Postnikov to give parameterizations of the positroid cells of the totally nonnegative Grassmannian \(\text {Gr}^{\ge 0}(n,k)\). Any two plabic graphs for the same positroid cell can be related by a sequence of certain moves. The flip graph has plabic graphs as vertices and has edges connecting the plabic graphs which are related

    更新日期:2020-02-17
  • Birational geometry of moduli spaces of stable objects on Enriques surfaces
    Sel. Math. (IF 1.053) Pub Date : 2020-02-13
    Thorsten Beckmann

    Using wall-crossing for K3 surfaces, we establish birational equivalence of moduli spaces of stable objects on generic Enriques surfaces for different stability conditions. As an application, we prove in the case of a Mukai vector of odd rank that they are birational to Hilbert schemes. The argument makes use of a new Chow-theoretic result, showing that moduli spaces on an Enriques surface give rise

    更新日期:2020-02-13
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