Counts of maps to Grassmannians and intersections on the moduli space of bundles
Algebraic Geometry
2007-05-23 v2
Abstract
We show that intersection numbers on the moduli space of stable bundles of coprime rank and degree over a smooth complex curve can be recovered as highest-degree asymptotics in formulas of Vafa-Intriligator type. In particular, we explicitly evaluate all intersection numbers appearing in the Verlinde formula. Our results are in agreement with previous computations of Witten, Jeffrey-Kirwan and Liu. Moreover, we prove the vanishing of certain intersections on a suitable Quot scheme which can be interpreted as giving equations between counts of maps to the Grassmannian.
Keywords
Cite
@article{arxiv.math/0602335,
title = {Counts of maps to Grassmannians and intersections on the moduli space of bundles},
author = {Alina Marian and Dragos Oprea},
journal= {arXiv preprint arXiv:math/0602335},
year = {2007}
}