Resolutions for Equivariant Sheaves over Toric Varieties

TL;DR

This paper develops a method to construct global resolutions for coherent equivariant sheaves on toric varieties using sheaves over posets, linking resolutions of sheaves to free resolutions of vector space arrangements.

Contribution

It introduces a novel framework of sheaves over posets and a gluing technique to build global resolutions for equivariant sheaves on toric varieties.

Findings

Constructed global resolutions for equivariant sheaves.

Established a correspondence between sheaf resolutions and vector space arrangements.

Provided a new approach to study sheaves on toric varieties.

Abstract

In this work we construct global resolutions for general coherent equivariant sheaves over toric varieties. For this, we use the framework of sheaves over posets. We develop a notion of gluing of posets and of sheaves over posets, which we apply to construct global resolutions for equivariant sheaves. Our constructions give a natural correspondence between resolutions for reflexive equivariant sheaves and free resolutions of vector space arrangements.