Mumford-Thaddeus Principle on the Moduli Space of Vector Bundles on an Algebraic Surface
alg-geom
2008-02-03 v1 Algebraic Geometry
Abstract
We study the behavior of the Gieseker space of semistable torsion-free sheaves of rank r and fixed c_1, c_2 on a non-singular projective surface as the polarization varies. It is shown that the ample cone admits a locally finite chamber structure, and that passing a wall adjacent to a pair of chambers has the effect of modifying the moduli space by a (finite) sequence of flips of the type studied by Thaddeus. The key steps are a modification of Simpson's method and the introduction of a "rationally twisted" moduli space. The result is more general but less explicit than the recent work of Ellingsrud-Goettsche (alg-geom/9410005) and Friedman-Qin (alg-geom/9410007).
Keywords
Cite
@article{arxiv.alg-geom/9410016,
title = {Mumford-Thaddeus Principle on the Moduli Space of Vector Bundles on an Algebraic Surface},
author = {K. Matsuki and R. Wentworth},
journal= {arXiv preprint arXiv:alg-geom/9410016},
year = {2008}
}
Comments
61 pages, amstex