2002/04/17 by Herbert Lange, H. Lange, Lange, H. +2
Mathematics · #14F05 #14H60 #32L10 #Algebraic Geometry (math.AG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AG #msc:14F05 #msc:14H60 #msc:32L10
paper · pdf · doi:10.48550/arxiv.math/0204216
11 pages
openalex publication_date 2002/04/17 · arxiv created 2002/05/03 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 (to appear in Commun. Math. Phys.) and our results answer a question raised in that paper. In this revised version some references are added.