Mathematische Annalen

, Volume 328, Issue 1–2, pp 121–133 | Cite as

Counting maximal subbundles via Gromov-Witten invariants

  • Yogish I. HollaEmail author


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


Projective Curve Stable Bundle Smooth Projective Curve Quot Scheme Maximal Subbundles 
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© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  1. 1.School of MathematicsTata Institute of Fundamental ResearchIndia

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