On bundles of rank 3 computing Clifford indices

Abstract

Let $C$ be a smooth irreducible projective algebraic curve defined over the complex numbers. The notion of the Clifford index of $C$ was extended a few years ago to[4] semistable bundles of any rank. Recent work has been focused mainly on the rank-$2$ Clifford index, although interesting results have also been obtained for the case of rank $3$. In this paper we extend this work, obtaining improved lower bounds for the rank-$3$ Clifford index. This allows the first computations of the rank-$3$ index in nontrivial cases and examples for which the rank-$3$ index is greater than the rank-$2$ index.