Asymptotics of Immaculate Line Bundles on Smooth Toric Deligne–Mumford Stacks

A line bundle is immaculate if its cohomology vanishes in every dimension. We give a criterion for when a smooth toric Deligne–Mumford stack has infinitely many immaculate line bundles. This answers positively a question of Borisov and Wang. As a byproduct, we describe the asymptotic behavior of the collection of immaculate line bundles.