On bundles of rank 3 computing Clifford indices

TL;DR

This paper extends the study of Clifford indices to rank-3 bundles on algebraic curves, providing improved bounds and new examples where the rank-3 index exceeds the rank-2 index.

Contribution

It introduces improved lower bounds for the rank-3 Clifford index and computes it in new non-trivial cases, advancing understanding of higher-rank Clifford indices.

Findings

Derived new lower bounds for rank-3 Clifford index

Computed the index for specific non-trivial cases

Found examples where rank-3 index exceeds rank-2 index

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 semistable bundles of any rank. Recent work has been focussed 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 non-trivial cases and examples for which the rank-3 index is greater than the rank-2 index.