Counterexamples to Mercat's Conjecture

Abstract

For any n>3, we provide examples of curves lying on K3 surfaces and vector bundles on those curves which invalidate Mercat's conjecture for rank n bundles.

6 pages, Proof of a lemma added in Section 2, Slight change in the proof of the main theorem, added references

References in corpus (3)

• Minimal resolutions, Chow forms and Ulrich bundles on K3 surfaces
• Lazarsfeld-Mukai bundles and applications
• Bundles of rank 2 with small Clifford index on algebraic curves