Maximal subbundles and Gromov invariants

Abstract

In this article we explicitly compute the number of maximal subbundles of rank $k$ of a generically stable bundle of rank $r$ and degree $d$ over a smooth projective curve $C$ of genus $g\ge 2$ over $\C$, when the dimension of the quot scheme of maximal subbundles is zero. Our method is to describe the this number purely in terms of the Gromov invariants of the Grassmannian and then use the formula of Vafa and Intriligator to compute them.

13 pages, References added

Cited by in corpus (2)

• On Frobenius-destabilized rank-2 vector bundles over curves
• Gauge theoretical Gromov-Witten invariants and virtual fundamental classes