Families of maximal subbundles of stable vector bundles on curves

Details Families of maximal subbundles of stable vector bundles on curves Families of maximal subbundles of stable vector bundles on curves

2000-05-10

arxiv.org/abs/math/0005097v1

Mathematics

Algebraic Geometry

8 pages, Latex

Scientific paper

Let X be a smooth projective curve of genus g bigger then 2. For any vector bundle E on X let M_k(E) be the scheme of all rank k subbundles of E with maximal degree. For every integers r, k and x with 0 r), we construct a rank r stable vector bundle E such that M_k(E) has an irreducible component of dimension x. Furthermore, if there exists a stable vector bundle F with small Lange's invariant s_k(F) and with M_k(F) `spread enough', then X i s a multiple covering of a curve of genus bigger then 2.

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