The gonality conjecture on syzygies of algebraic curves of large degree

2014/07/16 by Lawrence Ein, Robert Lazarsfeld, Ein, Lawrence +1 · 3 citations
Mathematics · Computer Science · #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1407.4445

Abstract

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.

Citations

• On the projective normality of complete linear series on an algebraic curve
• Asymptotic syzygies of algebraic varieties

Cited by

• Hierarchical structure of graded Betti numbers in the quadratic strand
• Vanishing of weight one syzygies of projective varieties
• Determinantal ideals of secant varieties

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• Linear syzygies on curves with prescribed gonality