Stable pairs, linear systems and the Verlinde formula
alg-geom
2008-02-03 v1 Algebraic Geometry
Abstract
We study the moduli problem of pairs consisting of a rank 2 vector bundle and a nonzero section over a fixed smooth curve. The stability condition involves a parameter; as it varies, we show that the moduli space undergoes a sequence of flips in the sense of Mori. As applications, we prove several results about moduli spaces of rank 2 bundles, including the Harder-Narasimhan formula and the SU(2) Verlinde formula. Indeed, we prove a general result on the space of sections of powers of the ideal sheaf of a curve in projective space, which includes the Verlinde formula.
Cite
@article{arxiv.alg-geom/9210007,
title = {Stable pairs, linear systems and the Verlinde formula},
author = {Michael Thaddeus},
journal= {arXiv preprint arXiv:alg-geom/9210007},
year = {2008}
}
Comments
40 pages, LaTeX