On Clifford's theorem for rank-3 bundles

Details On Clifford's theorem for rank-3 bundles On Clifford's theorem for rank-3 bundles

2003-10-29

arxiv.org/abs/math/0310463v1

Mathematics

Algebraic Geometry

15 pages

Scientific paper

In this paper we obtain bounds on $h^0(E)$ where $E$ is a semistable bundle of rank 3 over a smooth irreducible projective curve $X$ of genus $g \geq 2$ defined over an algebraically closed field of characteristic 0. These bounds are expressed in terms of the degrees of stability $s_1(E), s_2(E)$. We show also that in some cases the bounds are best possible. These results extend recent work of J. Cilleruelo and I. Sols for bundles of rank 2.

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