On Clifford’s theorem for rank-3 bundles

  • Christoph Scheven

    Friedrich-Alexander-Universität Erlangen, Germany
  • Peter E. Newstead

    University of Liverpool, UK


In this paper we obtain bounds on h0(E)h^0(E) where EE is a semistable bundle of rank 3 over a smooth irreducible projective curve XX of genus g2g \geq 2 defined over an algebraically closed field of characteristic 0. These bounds are expressed in terms of the degrees of stability s1(E)s_1(E), s2(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.

Cite this article

Christoph Scheven, Peter E. Newstead, On Clifford’s theorem for rank-3 bundles. Rev. Mat. Iberoam. 22 (2006), no. 1, pp. 287–304

DOI 10.4171/RMI/456