Koszul duality for toric varieties

TL;DR

This paper demonstrates a Koszul duality between categories of perverse sheaves on dual affine toric varieties, using explicit combinatorial constructions for mixed sheaves.

Contribution

It establishes a new explicit combinatorial framework for Koszul duality in the context of toric varieties, linking geometric and algebraic structures.

Findings

Categories of perverse sheaves on dual toric varieties are Koszul dual.

Explicit combinatorial functor constructed for this duality.

Provides new tools for understanding sheaf categories on toric varieties.

Abstract

We show that certain categories of perverse sheaves on a pair of affine toric varieties defined by dual cones are Koszul dual in the sense of Beilinson, Ginzburg and Soergel. The functor expressing this duality is constructed explicitly using a combinatorial model for mixed sheaves on toric varieties.