English

Subbundles of maximal degree

Algebraic Geometry 2009-11-10 v1

Abstract

Let E be a generic vector bundle of rank r and degree d on a generic curve of genus g. If r'd-rd'=r'(r-r')(g-1), the number of subbundles E' of E of rank r' and degree d' is finite. We present a new method to compute the number of such E' that consists in degenerating the curve to a reducible curve. We obtain very explicit formulae for r'=1 (Oxbury's Theorem) and also in the case r=4, r'=2.

Keywords

Cite

@article{arxiv.math/0307299,
  title  = {Subbundles of maximal degree},
  author = {Montserrat Teixidor i Bigas},
  journal= {arXiv preprint arXiv:math/0307299},
  year   = {2009}
}

Comments

To appear in Proceedings of the Cambridge Philosophical Society

R2 v1 2026-07-22T16:56:27.997Z