On $\mathrm{H}-$trivial line bundles on toric DM stacks of dimension two

TL;DR

This paper provides a combinatorial criterion to identify infinitely many line bundles with trivial cohomology on two-dimensional toric Deligne-Mumford stacks, and explores their structural properties.

Contribution

It introduces a new combinatorial criterion for trivial cohomology line bundles and analyzes their structure on 2D toric DM stacks.

Findings

Identifies conditions for infinitely many trivial cohomology line bundles

Provides a structural analysis of these line bundles

Enhances understanding of line bundle cohomology on toric stacks

Abstract

We study line bundles on toric DM stacks $\mathbb{P}_{\mathbf{\Sigma}}$ of dimension two. We give a combinatorial criterion of when infinitely many line bundles on $\mathbb{P}_{\mathbf{\Sigma}}$ have trivial cohomology. We further discuss the structure of the set of such line bundles.