Lower bounds for Clifford indices in rank three

TL;DR

This paper establishes lower bounds for the Clifford indices of rank 3 vector bundles on algebraic curves and demonstrates the existence of non-generated bundles computing these indices on certain plane curves.

Contribution

It provides new lower bounds for rank 3 Clifford indices and shows the existence of non-generated bundles computing these indices on smooth plane curves of degree at least 10.

Findings

Lower bounds for Clifford indices in rank 3 bundles are established.

Existence of non-generated bundles computing Clifford indices on plane curves of degree ≥10.

Results extend understanding of vector bundle properties on algebraic curves.

Abstract

Clifford indices for semistable vector bundles on a smooth projective curve of genus at least 4 were defined in previous papers of the authors. In the present paper, we establish lower bounds for the Clifford indices for rank 3 bundles. As a consequence we show that, on smooth plane curves of degree at least 10, there exist non-generated bundles of rank 3 computing one of the Clifford indices.