English

Intersection theory on moduli spaces of holomorphic bundles of arbitrary rank on a Riemann surface

alg-geom 2008-02-03 v2 dg-ga High Energy Physics - Theory Algebraic Geometry Differential Geometry

Abstract

We prove formulas (found by Witten in 1992 using physical methods) for intersection pairings in the cohomology of the moduli space M(n,d) of stable holomorphic vector bundles of rank n and degree d (assumed coprime) on a Riemann surface of genus g greater than or equal to 2. We also use these formulas for intersection numbers to obtain a proof of the Verlinde formula for the dimension of the space of holomorphic sections of a line bundle over M(n,d).

Keywords

Cite

@article{arxiv.alg-geom/9608029,
  title  = {Intersection theory on moduli spaces of holomorphic bundles of arbitrary rank on a Riemann surface},
  author = {Lisa C. Jeffrey and Frances C. Kirwan},
  journal= {arXiv preprint arXiv:alg-geom/9608029},
  year   = {2008}
}

Comments

77 pages, LaTeX version 2.09. This is the text of the revised version which will appear in Annals of Mathematics. An error in Section 2 of the previous version has been corrected