Mathematics – Algebraic Geometry
Scientific paper
2008-10-02
Mathematics
Algebraic Geometry
55 pages, third version, theorem matching Gieseker and GIT stability for torsion free sheaves in full generality added (Thm. 3
Scientific paper
Extending work of Klyachko and Perling, we develop a combinatorial description of pure equivariant sheaves of any dimension on an arbitrary nonsingular toric variety $X$. Using geometric invariant theory (GIT), this allows us to construct explicit moduli spaces of pure equivariant sheaves on $X$ corepresenting natural moduli functors (similar to work of Payne in the case of equivariant vector bundles). The action of the algebraic torus on $X$ lifts to the moduli space of all Gieseker stable sheaves on $X$ and we express its fixed point locus explicitly in terms of moduli spaces of pure equivariant sheaves on $X$. One of the problems arising is to find an equivariant line bundle on the side of the GIT problem, which precisely recovers Gieseker stability. In the case of torsion free equivariant sheaves, we can always construct such equivariant line bundles. As a by-product, we get a combinatorial description of the fixed point locus of the moduli space of $\mu$-stable reflexive sheaves on $X$. As an application, we show in a sequel \cite{Koo} how these methods can be used to compute generating functions of Euler characteristics of moduli spaces of $\mu$-stable torsion free sheaves on nonsingular complete toric surfaces.
Kool Martijn
No associations
LandOfFree
Fixed Point Loci of Moduli Spaces of Sheaves on Toric Varieties does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Fixed Point Loci of Moduli Spaces of Sheaves on Toric Varieties, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Fixed Point Loci of Moduli Spaces of Sheaves on Toric Varieties will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-492466