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 \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}.

I have added a section about parabolic sheaves Minor bug fixes

References in corpus (4)

• Smooth toric DM stacks
• Good moduli spaces for Artin stacks
• Grothendieck Duality for Deligne-Mumford Stacks
• Fibrés paraboliques et champ des racines

Cited by in corpus (6)

• Grothendieck Duality for Deligne-Mumford Stacks
• Instantons and framed sheaves on Kähler Deligne-Mumford stacks
• Relative orbifold Pandharipande-Thomas theory and the degeneration formula
• Moduli space of pairs over projective stacks
• Moduli Spaces of Coherent Sheaves on Projective Deligne-Mumford Stacks over Algebraic Spaces
• Embedding Deligne-Mumford stacks into GIT quotient stacks of linear representations