Lazarsfeld-Mukai bundles and applications

Abstract

We survey the development of the notion of Lazarsfeld-Mukai bundles together with various applications, from the classification of Mukai manifolds to Brill-Noether theory and syzygies of $K3$ sections. To see these techniques at work, we present a short proof of a result of M. Reid on the existence of elliptic pencils.

updated presentation, updated references, small correction on page 6. I. Peeva (ed.), Commutative Algebra: Expository Papers Dedicated to David Eisenbud on the Occasion of His 65th Birthday, Springer Science+Business Media New York 2013

References in corpus (2)

• Green's Conjecture for curves on arbitrary K3 surfaces
• Pencils of small degree on curves on unnodal Enriques surfaces

Cited by in corpus (6)

• Generalized Lazarsfeld-Mukai bundles and a conjecture of Donagi and Morrison
• On the Semistability of certain Lazarsfeld-Mukai bundles on Abelian surfaces
• Curves on Brill-Noether special K3 surfaces
• Lazarsfeld-Mukai bundles and applications. II
• Green's Conjecture for curves on rational surfaces with an anticanonical pencil
• Counterexamples to Mercat's Conjecture