On $\mathrm{H}-$trivial line bundles on toric DM stacks of dim $\geq3$

Abstract

We study line bundles on smooth toric DM stacks $\mathbb{P}_{\mathbf{\Sigma}}$ of arbitrary dimension. A sufficient condition is given for when infinitely many line bundles on $\mathbb{P}_{\mathbf{\Sigma}}$ have trivial cohomology. In dimension three, the sufficient condition is also a necessary condition in the case that $\mathbf{\Sigma}$ has no more than one pair of collinear rays.