Abstract
Let C be a nonsingular irreducible projective curve of genus g ≥ 2 defined over the complex numbers. Suppose that 1 ≤ n′ ≤ 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 (Commun. Math. Phys. 227 (2002), 551–585) and our results answer a question raised in that paper.
To C. S. Seshadri on his 70th birthday
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Lange, H., Newstead, P.E. (2003). Maximal Subbundles and Gromov-Witten Invariants. In: Lakshmibai, V., et al. A Tribute to C. S. Seshadri. Hindustan Book Agency, Gurgaon. https://doi.org/10.1007/978-93-86279-11-8_20
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DOI: https://doi.org/10.1007/978-93-86279-11-8_20
Publisher Name: Hindustan Book Agency, Gurgaon
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