Vector Bundles of Rank 2 Computing Clifford Indices

Abstract

Clifford indices of vector bundles on algebraic curves were introduced in a previous article of the authors. In this article 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.

Key Words:

• Clifford indices
• Gonality
• Semistable vector bundle

2010 Mathematics Subject Classification:

• Primary 14H60
• Secondary 14H45, 14H51

ACKNOWLEDGMENTS

Both authors are members of the research group VBAC (Vector Bundles on Algebraic Curves). The second author would like to thank the Department Mathematik der Universität Erlangen-Nürnberg for its hospitality.

Notes

Communicated by L. Ein.