Moduli Spaces of Semistable Sheaves on Projective Deligne-Mumford Stacks
arXiv:0811.1949
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 \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}.
arXiv commentI have added a section about parabolic sheaves Minor bug fixes
References in corpus (4)
Cited by in corpus (13)
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- Relative orbifold Pandharipande-Thomas theory and the degeneration formula
- The Vafa-Witten invariants via surface Deligne-Mumford stacks and S-duality
- Moduli spaces of semistable pairs on projective Deligne-Mumford stacks
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- Embedding Deligne-Mumford stacks into GIT quotient stacks of linear representations
- Moduli Spaces of Coherent Sheaves on Projective Deligne-Mumford Stacks over Algebraic Spaces
- Moduli of parabolic sheaves on a polarized logarithmic scheme