Equivariant exceptional collections on smooth toric stacks

TL;DR

This paper constructs full exceptional collections in the derived categories of torus-equivariant coherent sheaves on smooth toric varieties and stacks, revealing their dependence on the PL homeomorphism type of associated simplicial complexes.

Contribution

It introduces explicit constructions of full exceptional collections for these categories and shows their dependence solely on the PL homeomorphism type.

Findings

Full exceptional collections are constructed for categories on smooth toric varieties and stacks.

The derived categories depend only on the PL homeomorphism type of the simplicial complex.

Provides new insights into the structure of equivariant derived categories.

Abstract

We study the bounded derived categories of torus-equivariant coherent sheaves on smooth toric varieties and Deligne-Mumford stacks. We construct and describe full exceptional collections in these categories. We also observe that these categories depend only on the PL homeomorphism type of the corresponding simplicial complex.