Revista Matemática Iberoamericana

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Volume 22, Issue 1, 2006, pp. 287–304
DOI: 10.4171/RMI/456

Published online: 2006-04-30

On Clifford’s theorem for rank-3 bundles

Christoph Scheven[1] and Peter E. Newstead[2]

(1) Friedrich-Alexander-Universität Erlangen, Germany
(2) University of Liverpool, UK

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.

Keywords: Vector bundle, subbundle

Scheven Christoph, Newstead Peter: On Clifford’s theorem for rank-3 bundles. Rev. Mat. Iberoam. 22 (2006), 287-304. doi: 10.4171/RMI/456