Moduli Spaces of Semistable Sheaves on Projective Deligne-Mumford Stacks
By Fabio Nironi. 2008
52 citations recorded by the source corpus.
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}.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/2b831896f6ab81d7ce47b596a11dc6874ae438dc
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
In Geometry and Topology
Citations in the corpus
- Local Systems on Proper Algebraic V -manifolds (2010, background): “Suppose X is a smooth proper and separated DMstack of finite type and D ⊂ X a divisor with normal crossings.”
- Grothendieck Duality for Deligne-Mumford Stacks (2008, methodology): “ the cotangent complex shifted by the dimension of the stack as it is in the scheme theoretic setup. This paper has been partially motivated by our study on semistable sheaves on projective stacks in [NF08]. In particular we have used Grothendieck duality to handle the definition of dual sheaf in the”
- Good Moduli Spaces for Artin Stacks (2008, methodology): “Part (iii) was proved in the case of tame Artin stacks in [34] by using the local structure theorem of [1] to reduce to the case of a quotient stack of an affine scheme by a finite linearly reductive group scheme.”