On Clifford's theorem for rank-3 bundles

H. Lange; P. E. Newstead

paper

On Clifford's theorem for rank-3 bundles

arXiv:math/0310463

Abstract

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.

15 pages