Moduli Spaces of Semistable Sheaves on Projective Deligne-Mumford Stacks
Abstract
We introduce a notion of Gieseker stability for coherent sheaves on tame Deligne-Mumford stacks with projective moduli scheme and some chosen generating sheaf on the stack in the sense of Olsson and Starr MR2007396. We prove that this stability condition is open, and pure dimensional semistable sheaves form a bounded family. We explicitly construct the moduli stack of semistable sheaves as a finite type global quotient, and study the moduli scheme of stable sheaves and its natural compactification in the same spirit as the seminal paper of Simpson MR1307297. With this general machinery we are able to retrieve, as special cases, results of Lieblich MR2309155 and Yoshioka MR2306170 about moduli of twisted sheaves and parabolic stability introduced by Maruyama-Yokogawa in MR1162674.