On Clifford’s theorem for rank-3 bundles

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