English

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.

Keywords

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

R2 v1 2026-07-22T07:41:07.325Z