• 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：2020-07-29
• 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
• 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：2020-07-21
• 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
• 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
• 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
• 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
• 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
• 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：2020-07-07
• 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
• 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
• 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
• 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：2020-06-23
• 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：2020-06-23
• Sel. Math. (IF 1.053) Pub Date : 2020-06-22

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：2020-06-23
• 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：2020-06-18
• 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
• Sel. Math. (IF 1.053) Pub Date : 2020-06-12

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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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：2020-04-23
• 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：2020-04-23
• 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：2020-04-23
• 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：2020-04-23
• 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：2020-04-23
• 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：2020-04-23
• 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：2020-04-23
• 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：2020-04-23
• 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：2020-04-23
• 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：2020-04-23
• 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：2020-04-23
• 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：2020-04-23
• 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：2020-04-23
• 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：2020-04-23
• 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：2020-04-23
• 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：2020-04-23 • 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：2020-04-23
• 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：2020-04-23
• 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：2020-04-23
• Sel. Math. (IF 1.053) Pub Date : 2020-01-28
We prove that the roots of a smooth monic polynomial with complex-valued coefficients defined on a bounded Lipschitz domain $$\Omega$$ in $$\mathbb {R}^m$$ admit a parameterization by functions of bounded variation uniformly with respect to the coefficients. This result is best possible in the sense that discontinuities of the roots are in general unavoidable due to monodromy. We show that the discontinuity