Related papers: Resolutions for Equivariant Sheaves over Toric Var…
Over a smooth projective toric variety we study toric sheaves, that is, reflexive sheaves equivariant with respect to the acting torus, from a polyhedral point of view. One application is the explicit construction of the torus invariant…
Toric prevarieties are non-separated analogues of toric varieties. Perling \cite{Perling_equivariant_sheaves_tor_var} provided a combinatorial description of equivariant quasicoherent sheaves on toric varieties, extending earlier ideas of…
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…
We study global primary decompositions in the category of sheaves on a scheme which are equivariant under the action of an algebraic group. We show that equivariant primary decompositions exist if the group is connected. As main application…
In this article we review some recent developments in heterotic compactifications. In particular we review an ``inherently toric'' description of certain sheaves, called equivariant sheaves, that has recently been discussed in the physics…
In this note we derive a formalism for describing equivariant sheaves over toric varieties. This formalism is a generalization of a correspondence due to Klyachko, which states that equivariant vector bundles on toric varieties are…
We develop a theory of general sheaves over weighted projective lines. We define and study a canonical decomposition, analogous to Kac's canonical decomposition for representations of quivers, study subsheaves of a general sheaf, general…
Extending work of Klyachko and Perling, we develop a combinatorial description of pure equivariant sheaves of any dimension on an arbitrary nonsingular toric variety $X$. Using geometric invariant theory (GIT), this allows us to construct…
We give a complete classification of equivariant vector bundles of rank two over smooth complete toric surfaces and construct moduli spaces of such bundles. This note is a direct continuation of an earlier note where we developed a general…
We construct generalized Weyman complexes for coherent sheaves on projective space and describe explicitly how the differential depend on the differentials in the correpsonding Tate resolution. We apply this to define the Weyman complex of…
In this paper we introduce a generalisation of a covariant Grothendieck construction to the setting of sites. We study the basic properties of defined site structures on Grothendieck constructions as well as we treat the cohomological…
This article is based on my lecture notes from summer schools at the Universities of Utah (June 2007) and Warwick (September 2007). We provide an introduction to explicit methods in the study of moduli spaces of quiver representations and…
The aim of this paper is to discuss a combinatorial characterisation of stability for toric vector bundles (or equivariant reflexive sheaves) in the terms of their parliaments of polytopes, a generalization of moment polytopes for toric…
We describe categories of equivariant vector bundles on certain toroidal spherical varieties in linear algebra terms: vector spaces equipped with filtrations, group and Lie algebra actions, and linear maps preserving these structures.
We describe the Tate resolution of a coherent sheaf or complex of coherent sheaves on a product of projective spaces. Such a resolution makes explicit all the cohomology of all twists of the sheaf, including, for example, the multigraded…
The classification of equivariant toroidal embeddings of a reductive group over an algebraically closed field is combinatorial and does not depend on the characteristic of the base field. This suggests that there should exist ``universal''…
In this paper we give an inherently toric description of a special class of sheaves (known as equivariant sheaves) over toric varieties, due in part to A. A. Klyachko. We apply this technology to heterotic compactifications, in particular…
Studying toric varieties from a scheme-theoretical point of view leads to toric schemes, i.e. "toric varieties over arbitrary base rings". It is shown how the base ring affects the geometry of a toric scheme. Moreover, generalisations of…
We characterize embeddability of algebraic varieties into smooth toric varieties and prevarieties. Our embedding results hold also in an equivariant context and thus generalize a well known embedding theorem of Sumihiro on quasiprojective…
Here we construct spaces of coinvariants for Heisenberg vertex algebras on abelian varieties and show that these globalize to twisted $\mathscr{D}$-modules on the moduli space of abelian varieties. Remarkably, we recover the standard…