Subbundles of maximal degree

Details Subbundles of maximal degree Subbundles of maximal degree

2003-07-22

arxiv.org/abs/math/0307299v1

Mathematics

Algebraic Geometry

To appear in Proceedings of the Cambridge Philosophical Society

Scientific paper

10.1017/S0305004103007370

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.

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