• Sel. Math. (IF 1.053) Pub Date : 2021-01-16
Thomas Reichelt, Morihiko Saito, Uli Walther

We construct complex projective schemes with Lyubeznik numbers of their cones depending on the choices of projective embeddings. This answers a question of G. Lyubeznik in the characteristic 0 case. It contrasts with a theorem of W. Zhang in the positive characteristic case where the Frobenius endomorphism is used. Reducibility of schemes is essential in our argument. B. Wang recently constructed examples

更新日期：2021-01-18
• Sel. Math. (IF 1.053) Pub Date : 2021-01-13
Kevin McGerty, Thomas Nevins

To a quiver Q and choices of nonzero scalars $$q_i$$, non-negative integers $$\alpha _i$$, and integers $$\theta _i$$ labeling each vertex i, Crawley-Boevey–Shaw associate a multiplicative quiver variety $${\mathcal {M}}_\theta ^q(\alpha )$$, a trigonometric analogue of the Nakajima quiver variety associated to Q, $$\alpha$$, and $$\theta$$. We prove that the pure cohomology, in the Hodge-theoretic

更新日期：2021-01-13
• Sel. Math. (IF 1.053) Pub Date : 2021-01-07
Fei Xie

We provide a semiorthogonal decomposition for the derived category of fibrations of quintic del Pezzo surfaces with rational Gorenstein singularities. There are three components, two of which are equivalent to the derived categories of the base and the remaining non-trivial component is equivalent to the derived category of a flat and finite of degree 5 scheme over the base. We introduce two methods

更新日期：2021-01-08
• Sel. Math. (IF 1.053) Pub Date : 2021-01-06
Jeffrey Hicks

We look at how one can construct from the data of a dimer model a Lagrangian submanifold in $$(\mathbb {C}^*)^n$$ whose valuation projection approximates a tropical hypersurface. Each face of the dimer corresponds to a Lagrangian disk with boundary on our tropical Lagrangian submanifold, forming a Lagrangian mutation seed. Using this we find tropical Lagrangian tori $$L_{T^2}$$ in the complement of

更新日期：2021-01-07
• Sel. Math. (IF 1.053) Pub Date : 2021-01-05
James Tao

Let X be a smooth algebraic variety over k. We prove that any flat quasicoherent sheaf on $${\text {Ran}}(X)$$ canonically acquires a $$\mathscr {D}$$-module structure. In addition, we prove that, if the geometric fiber $$X_{\overline{k}}$$ is connected and admits a smooth compactification, then any line bundle on $$S \times {\text {Ran}}(X)$$ is pulled back from S, for any locally Noetherian k-scheme

更新日期：2021-01-05
• Sel. Math. (IF 1.053) Pub Date : 2021-01-04
Michael Perlman, Claudiu Raicu

We determine explicitly the Hodge ideals for the determinant hypersurface as an intersection of symbolic powers of determinantal ideals. We prove our results by studying the Hodge and weight filtrations on the mixed Hodge module $$\mathcal {O}_{\mathscr {X}}(*\mathscr {Z})$$ of regular functions on the space $$\mathscr {X}$$ of $$n\times n$$ matrices, with poles along the divisor $$\mathscr {Z}$$ of

更新日期：2021-01-04
• Sel. Math. (IF 1.053) Pub Date : 2020-11-26
Manuel Krannich

We compute the mapping class group of the manifolds $$\sharp ^g(S^{2k+1}\times S^{2k+1})$$ for $$k>0$$ in terms of the automorphism group of the middle homology and the group of homotopy $$(4k+3)$$-spheres. We furthermore identify its Torelli subgroup, determine the abelianisations, and relate our results to the group of homotopy equivalences of these manifolds.

更新日期：2020-11-27
• Sel. Math. (IF 1.053) Pub Date : 2020-11-19
Somnath Jha, Tadashi Ochiai

Let $$K_\infty$$ be a p-adic Lie extension of a number field K which fits into the setting of non-commutative Iwasawa theory formulated by Coates–Fukaya–Kato–Sujatha–Venjakob. For the first main result, we will prove the control theorem of Selmer group associated to a motive, which generalizes previous results by the second author and Greenberg. As an application of this control theorem, we prove

更新日期：2020-11-19
• Sel. Math. (IF 1.053) Pub Date : 2020-11-17
Johannes Schmitt, Jason van Zelm
更新日期：2020-11-17
• Sel. Math. (IF 1.053) Pub Date : 2020-11-12
Erman Çineli, Viktor L. Ginzburg, Başak Z. Gürel

We prove a variant of the Chance–McDuff conjecture for pseudo-rotations: under certain additional conditions, a closed symplectic manifold which admits a Hamiltonian pseudo-rotation must have deformed quantum product and, in particular, some non-zero Gromov–Witten invariants. The only assumptions on the manifold are that it is weakly monotone and that its minimal Chern number is at least two. The conditions

更新日期：2020-11-13
• Sel. Math. (IF 1.053) Pub Date : 2020-11-12
Christian Gaetz, Yibo Gao

Björner and Ekedahl (Ann Math (2) 170(2):799–817, 2009) prove that general intervals [e, w] in Bruhat order are “top-heavy”, with at least as many elements in the i-th corank as the i-th rank. Well-known results of Carrell (in: Algebraic groups and their generalizations: classical methods (University Park, PA, 1991), volume 56 of proceedings of symposium on pure mathematics, pp 53–61. American Mathematical

更新日期：2020-11-12
• Sel. Math. (IF 1.053) Pub Date : 2020-11-04
Aron Heleodoro

We construct a map from the prestack of Tate objects over a commutative ring k to the stack of $${\mathbb {G}}_{\mathrm{m}}$$-gerbes. The result is obtained by combining the determinant map from the stack of perfect complexes as proposed by Schürg–Toën–Vezzosi with a relative $$S_{\bullet }$$-construction for Tate objects as studied by Braunling–Groechenig–Wolfson. Along the way we prove a result about

更新日期：2020-11-04
• Sel. Math. (IF 1.053) Pub Date : 2020-10-31
Alexander Yom Din

I am grateful to D. Gaitsgory for pointing out the mistake.

更新日期：2020-11-02
• Sel. Math. (IF 1.053) Pub Date : 2020-10-28
Jonathan Brundan, Alistair Savage, Ben Webster

We show that any Abelian module category over the (degenerate or quantum) Heisenberg category satisfying suitable finiteness conditions may be viewed as a 2-representation over a corresponding Kac–Moody 2-category (and vice versa). This gives a way to construct Kac–Moody actions in many representation-theoretic examples which is independent of Rouquier’s original approach via “control by $$K_0$$.”

更新日期：2020-10-30
• Sel. Math. (IF 1.053) Pub Date : 2020-10-23
Damien Calaque, Martin Gonzalez

We construct a twisted version of the genus one universal Knizhnik–Zamolodchikov–Bernard (KZB) connection introduced by Calaque–Enriquez–Etingof, that we call the ellipsitomic KZB connection. This is a flat connection on a principal bundle over the moduli space of $$\Gamma$$-structured elliptic curves with marked points, where $$\Gamma ={{\mathbb {Z}}}/M{{\mathbb {Z}}}\times {{\mathbb {Z}}}/N{{\mathbb 更新日期：2020-10-30 • 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 • 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 • 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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 • 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 • 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 • 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 • 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：2020-07-20
• 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：2020-07-06
• 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：2020-06-22
• 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
• 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：2020-06-22
• 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
• 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
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
• 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：2020-04-18
• 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
• 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
• 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
• 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
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