Moduli Spaces of Semistable Sheaves on Projective Deligne-Mumford Stacks

Details Moduli Spaces of Semistable Sheaves on Projective Deligne-Mumford Stacks Moduli Spaces of Semistable Sheaves on Projective Deligne-Mumford Stacks

2008-11-12

arxiv.org/abs/0811.1949v2

Mathematics

Algebraic Geometry

I have added a section about parabolic sheaves Minor bug fixes

Scientific paper

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 \cite{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 \cite{MR1307297}. With this general machinery we are able to retrieve, as special cases, results of Lieblich \cite{MR2309155} and Yoshioka \cite{MR2306170} about moduli of twisted sheaves and parabolic stability introduced by Maruyama-Yokogawa in \cite{MR1162674}.

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