Maximal Subbundles and Gromov-Witten Invariants

H. Lange; P. E. Newstead

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arXiv · math/0204216

Maximal Subbundles and Gromov-Witten Invariants

H. Lange·P. E. Newstead

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Abstract

Let $C$ be a nonsingular irreducible projective curve of genus $g\ge2$ defined over the complex numbers. Suppose that $1\le n'\le n-1$ and $n'd-nd'=n'(n-n')(g-1)$. It is known that, for the general vector bundle $E$ of rank $n$ and degree $d$, the maximal degree of a subbundle of $E$ of rank $n'$ is $d'$ and that there are finitely many such subbundles. We obtain a formula for the number of these maximal subbundles when $(n',d')=1$. For $g=2$, $n'=2$, we evaluate this formula explicitly. The numbers computed here are Gromov-Witten invariants in the sense of a recent paper of Ch. Okonek and A. Teleman (to appear in Commun. Math. Phys.) and our results answer a question raised in that paper. In this revised version some references are added.

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BibTeX RIS

H. Lange, P. E. Newstead. 2002-05-03. Maximal Subbundles and Gromov-Witten Invariants. https://arxiv.org/abs/math/0204216

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