相关论文: Resolutions for Equivariant Sheaves over Toric Var…

We develop a new approach to the study of supersymmetric gauge theories on ALE spaces using the theory of framed sheaves on root toric stacks, which illuminates relations with gauge theories on $\mathbb{R}^4$ and with two-dimensional…

A toric vector bundle $\mathcal{E}$ is a torus equivariant vector bundle on a toric variety. We give a valuation theoretic and tropical point of view on toric vector bundles. We present three (equivalent) classifications of toric vector…

We formulate a version of Beck's monadicity theorem for abelian categories, which is applied to the equivariantization of abelian categories with respect to a finite group action. We prove that the equivariantization is compatible with the…

These are expanded notes on a lecture of the same title at the 2015 AMS summer institute in algebraic geometry. We give an introduction and overview of the "beyond geometric invariant theory" program for analyzing moduli problems in…

Achar has recently introduced a family of t-structures on the derived category of equivariant coherent sheaves on a $G$-scheme, generalizing the perverse coherent t-structures of Bezrukavnikov and Deligne. They are called \emph{staggered}…

We generalise Bogomolov's inequality to all coherent torsion-free sheaves on a smooth projective surface.

We study $T$-linear schemes, a class of objects that includes spherical and Schubert varieties. We provide a localization theorem for the equivariant Chow cohomology of these schemes that does not depend on resolution of singularities.…

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…

Let G be a finite subgroup of GL_n(C). A study is made of the ways in which resolutions of the quotient space C^n / G can parametrise G-constellations, that is, G-regular finite length sheaves. These generalise G-clusters, which are used in…

We define an equivalence relation among coherent sheaves on a projective variety called biliaison. We prove the existence of sheaves that are minimal in a biliaison class in a suitable sense, and show that all sheaves in the same class can…

We provide a framework for the construction of diffeomorphism invariant sheaves of nonlinear generalized functions spaces. As an application, global algebras of generalized functions for distributions on manifolds and diffeomorphism…

Using the language of stacks, we recast and generalize a selection of results in equivariant geometry.

We introduce a toric version of the sheaf of logarithmic vector fields along a divisor of a simplicial toric variety. The notion is also relevant for algebraically independent families of polynomials in the Cox ring. We provide a…

In this paper we derive an explicit version of the Bernstein-Gel'fand-Gel'fand (BGG) correspondence between bounded complexes of coherent sheaves on projective space and minimal doubly infinite free resolutions over its ``Koszul dual''…

This paper gives an explicit computation of the category of constructible sheaves on a toric variety (with respect to the stratification by torus orbits). Over the complex numbers, this simplifies a description due to Braden and Lunts. The…

Improved local and global versions of the effective Nullstellensatz for ideal sheaves on non-singular complex varieties are obtained, based on a new invariant motivated by the notion of finite type from the theory of several complex…

Let $\text{X}$ denote a projective variety over an algebraically closed field on which a linear algebraic group acts with finitely many orbits. Then, a conjecture of Soergel and Lunts in the setting of Koszul duality and Langlands'…

This paper is devoted to the study of some coherent sheaves on non reduced curves that can be locally embedded in smooth surfaces. If Y is such a curve then there is a filtration by subschemes C_i such that C_1 is the reduced curve…

We introduce an original notion of extra-fine sheaf on a topological space, and a variant (hyper-extra-fine) for which \v{C}ech cohomology in strictly positive degree vanishes. We provide a characterization of such sheaves when the…

We study derived categories of coherent sheaves on abelian varieties. We give a criterion for the equivalence of the derived categories on two abelian varieties. We describe the autoequivalence group for the derived category of coherent…