Related papers: Ansatz for $(-1)^{n-1}\nabla p_n$

We give a description of certain categories of equivariant coherent sheaves on Grothendieck's resolution in terms of the categorical affine Hecke algebra of Soergel. As an application, we deduce a relationship of these coherent sheaf…

Let R_n be the ring of coinvariants for the diagonal action of the symmetric group S_n. It is known that the character of R_n as a doubly-graded S_n module can be expressed using the Frobenius characteristic map as \nabla e_n, where e_n is…

The integral cohomology ring of the Hilbert scheme of n-tuples on the affine plane is shown to be isomorphic to the graded ring associated to a filtration of the ring of integral class functions on the symmetric group.

The sheaf-function correspondence identifies the group of constructible functions on a real analytic manifold $M$ with the Grothendieck group of constructible sheaves on $M$. When $M$ is a finite dimensional real vector space,…

We introduce a new class of smooth correspondences between Nakajima quiver varieties called split parabolic quiver varieties, and study their properties. We use these correspondences to construct an explicit resolution of singularities of…

Let $X$ be a complex smooth projective variety, and $\mathcal{G}$ a locally free sheaf on $X$. We show that there is a 1-to-1 correspondence between pairs $(\Lambda,\Xi)$, where $\Lambda$ is a sheaf of almost polynomial filtered algebras…

Let S be a K3 surface and Aut D(S) the group of auto-equivalences of the derived category of S. We construct a natural representation of Aut D(S) on the cohomology of all moduli spaces of stable sheaves (with primitive Mukai vectors) on S.…

In this paper, we develope an equivariant theory of Chern characters for coherent sheaves on compact complex manifolds with finite group actions, taking values in Bott-Chern cohomology classes. Furthermore, we establish the corresponding…

We give an explicit affine algebraic variety whose coordinate ring is isomorphic (as an algebra with the action of the Weyl group) with the equivariant cohomology of some Springer fibers.

Dosi and, quite recently, the author showed that, on the character space of a nilpotent Lie algebra, there exists a sheaf of Fr\'echet--Arens--Michael algebras (of noncommutative holomorphic functions in the complex case and of…

We study the coherent cohomology of automorphic sheaves corresponding to Siegel modular forms $f$ of low weight on ${\rm GSp}(4)$ Shimura varieties. Inspired by the work of Prasanna--Venkatesh on singular cohomology of locally symmetric…

We show that for any constructible sheaf F on a smooth algebraic variety X over a field of arbitrary characteristic its singular support SS(F) is equidimensional of dimension dim X. Here SS(F) is the minimal closed subset of the cotangent…

In this article, we study the cohomology of some analytic sheaves on the complementary in the projective space of a suitable infinite collection of hyperplane like the Drinfel'd symetric space. In particular, the sheaf of invertible…

We explain the precise relationship between two module-theoretic descriptions of sheaves on an involutive quantale, namely the description via so-called Hilbert structures on modules and that via so-called principally generated modules. For…

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…

For each braid $\beta\in Br_n$ we construct a $2$-periodic complex $\mathbb{S}_\beta$ of quasi-coherent $\mathbb{C}^*\times \mathbb{C}^*$-equivariant sheaves on the non-commutative nested Hilbert scheme $Hilb_{1,n}^{free}$. We show that the…

We determine the two-point invariants of the equivariant quantum cohomology of the Hilbert scheme of points of surface resolutions associated to type A_n singularities. The operators encoding these invariants are expressed in terms of the…

Let $C$ be a completely algebraic closed non-archimedean field over $\mathbb{Q}_p$ and $\alpha,r$ be two positive integers. Denote by $B_\alpha$ the ring $\mathbb{B}_{\mathrm{dR}}^+(C)/(\ker\theta)^\alpha$. This paper first constructs a…

Let $f: X \to S$ be flat morphism over an algebraically closed field $k$ with a relative normal crossings divisor $Y\subset X$, $(E, \nabla)$ be a bundle with a connection with log poles along $Y$ and curvature with values in…

We study equivariant resolutions and local cohomologies of toric sheaves for affine toric varieties, where our focus is on the construction of new examples of decomposable maximal Cohen-Macaulay modules of higher rank. A result of Klyachko…