Vector bundles of rank 2 computing Clifford indices

TL;DR

This paper investigates rank 2 vector bundles that compute Clifford indices on algebraic curves, providing insights into their properties and addressing recent counterexamples to Mercat's conjecture.

Contribution

It offers a detailed study of rank 2 bundles computing Clifford indices, advancing understanding of their structure and implications for algebraic geometry.

Findings

Identification of conditions under which rank 2 bundles compute Clifford indices

Analysis of counterexamples to Mercat's conjecture

Insights into the geometry of vector bundles on algebraic curves

Abstract

Clifford indices of vector bundles on algebraic curves were introduced in a previous paper of the authors. In this paper we study bundles of rank 2 which compute these Clifford indices. This is of particular interest in the light of recently discovered counterexamples to a conjecture of Mercat.