Movable curve classes and slope stability on Deligne-Mumford stacks

Abstract

We generalize some results in the literature on movable curve classes and slope stability of coherent sheaves on smooth projective varieties to the case of smooth proper DM stacks admitting projective coarse moduli spaces. As an application, we establish a Bogomolov-Gieseker inequality on such stacks. This paper is the second in a series aiming to generalize results of Popa-Schnell and Wei-Wu on Viehweg hyperbolicity to the setting of DM stacks, and in particular, to certain KSBA moduli spaces.