Equivariant sheaves on toric prevarieties

TL;DR

This paper extends the combinatorial description of equivariant quasicoherent sheaves from toric varieties to the more general setting of toric prevarieties, which are non-separated analogues.

Contribution

It provides a new combinatorial framework for understanding equivariant quasicoherent sheaves on toric prevarieties, building on prior work on toric varieties.

Findings

Extended Klyachko's framework to toric prevarieties.

Provided explicit combinatorial descriptions for sheaves on non-separated toric structures.

Bridged the gap between toric varieties and prevarieties in sheaf theory.

Abstract

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extending earlier ideas of Klyachko, who outlined a general framework for equivariant torsion free sheaves in an unpublished work \cite{kly_sheaf}. In this article, we present a combinatorial description of equivariant quasicoherent sheaves on toric prevarieties.