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

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.

20 pages, 8 figures