Green-Lazarsfeld's Conjecture for Generic Curves of Large Gonality

Abstract

We use Green's canonical syzygy conjecture for generic curves to prove that the Green-Lazarsfeld gonality conjecture holds for generic curves of genus g, and gonality d, if $g/3<d<[g/2]+2$.

5 pages

References in corpus (1)

• On the vanishing of higher syzygies of curves

Cited by in corpus (11)

• Asymptotic syzygies of algebraic varieties
• Remarks on syzygies of $d$-gonal curves
• Green's Conjecture for curves on arbitrary K3 surfaces
• Koszul cohomology and applications to moduli
• Gonality, apolarity and hypercubics
• The gonality conjecture on syzygies of algebraic curves of large degree
• On Green and Green-Lazarfeld conjectures for simple coverings of algebraic curves
• Linear syzygies of curves in weighted projective space
• Koszul cohomology and singular curves
• P^r-scrolls arising from Brill-Noether theory and K3-surfaces
• Singular curves on a K3 surface and linear series on their normalizations