Faisceaux pervers sur les vari\'et\'es toriques lisses

TL;DR

This paper provides a description of the category of perverse sheaves on smooth toric varieties using quiver representations derived from the fan structure, establishing an equivalence between these categories.

Contribution

It introduces a novel quiver-based framework to classify perverse sheaves on smooth toric varieties, linking geometric stratifications to algebraic representations.

Findings

Equivalence between perverse sheaves and quiver representations

Explicit description of the category Perv_X for smooth toric varieties

Framework applicable to stratified toric varieties

Abstract

Let X be a smooth toric variety stratified by the torus action. This paper is a presentation of a description of the category Perv_X of perverse sheaves on X relatively to the fixed stratification. We define a category of representations of a quiver, defined thanks to the fan of X, equivalent to Perv_X.