Acyclic toric sheaves

TL;DR

This paper establishes an explicit sufficient condition for certain torus-linearised reflexive sheaves on smooth projective toric varieties to be acyclic, generalizing previous theorems using Weil decorations.

Contribution

It introduces a new criterion for acyclicity of toric sheaves, extending Perlman and Smith's theorem with explicit conditions involving Weil decorations.

Findings

Provides an explicit sufficient condition for acyclicity of toric sheaves.

Generalizes a theorem of Perlman and Smith.

Uses Weil decorations to characterize acyclicity.

Abstract

Let $\mathcal E$ be a torus-linearised reflexive sheaf over a smooth projective toric variety. Generalising a theorem of Perlman and Smith, we prove an explicit sufficient condition for $\mathcal E$ to be acyclic via Weil decorations.