Bundles of rank 3 on curves of Clifford index 3

TL;DR

This paper extends previous work on the Clifford index for rank 3 vector bundles on curves, proving Mercat's conjecture for certain genera when the curve has Clifford index 3.

Contribution

It generalizes earlier results to curves with Clifford index 3, confirming Mercat's conjecture for rank 3 bundles in specific genus ranges.

Findings

Proves Mercat's conjecture for genus g ≤ 8 and g ≥ 13 with Clifford index 3.

Provides complete results for genus 7.

Extends previous bounds on Clifford index for rank 3 bundles.

Abstract

Two definitions of the Clifford index for vector bundles on a smooth projective curve $C$ of genus $g\ge4$ were introduced in a previous paper by the authors. In another paper the authors obtained results on one of these indices for bundles of rank 3. In this paper we extend these results in the case where $C$ has classical Clifford index 3. In particular we prove Mercat's conjecture for bundles of rank 3 for $g \leq 8$ and $g \geq 13$ when $C$ has classical Clifford index 3. We obtain complete results in the case of genus 7.