• Sel. Math. (IF 1.248) 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 1.248) 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 1.248) 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 1.248) 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 1.248) 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 1.248) 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 1.248) 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 1.248) 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 1.248) 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 1.248) 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 1.248) 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 1.248) 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 1.248) 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 1.248) 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 1.248) 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 1.248) 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 1.248) 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 1.248) 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 1.248) 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 1.248) 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 1.248) 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