The gonality conjecture on syzygies of algebraic curves of large degree

By L. Ein, R. Lazarsfeld. Publications mathématiques (Bures-sur-Yvette), 2014

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We show that a small variant of the methods used by Voisin in her study of canonical curves leads to a surprisingly quick proof of the gonality conjecture of Green and the second author, asserting that one can read off the gonality of a curve C from its resolution in the embedding defined by any one line bundle of sufficiently large degree. More generally, we establish a necessary and sufficient condition for the asymptotic vanishing of the weight one syzygies of the module associated to an arbitrary line bundle on C.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

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