Maximal Subbundles and GromovWitten Invariants
Abstract
Let $C$ be a nonsingular irreducible projective curve of genus $g\ge2$ defined over the complex numbers. Suppose that $1\le n'\le n1$ and $n'dnd'=n'(nn')(g1)$. 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 GromovWitten 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 April 2002
 DOI:
 10.48550/arXiv.math/0204216
 arXiv:
 arXiv:math/0204216
 Bibcode:
 2002math......4216L
 Keywords:

 Algebraic Geometry;
 14H60;
 14F05;
 32L10
 EPrint:
 11 pages