Generation of vector bundles computing Clifford indices

TL;DR

This paper investigates vector bundles that compute Clifford indices on smooth projective curves, demonstrating that under certain conditions, these bundles and their Serre duals are generated, advancing understanding of their structure.

Contribution

It provides new results on the generation properties of vector bundles computing Clifford indices and their Serre duals under specific conditions on the curve.

Findings

Bundles computing Clifford indices are generated under certain conditions.

Their Serre duals are also generated when specific criteria are met.

The study extends understanding of the structure of vector bundles related to Clifford indices.

Abstract

Clifford indices for semistable vector bundles on a smooth projective curve of genus at least 4 were defined in a previous paper of the authors. The present paper studies bundles which compute these Clifford indices. We show that under certain conditions on the curve all such bundles and their Serre duals are generated.