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

TL;DR

This paper proves the Green-Lazarsfeld gonality conjecture for generic curves with large gonality using Green's canonical syzygy conjecture, establishing new bounds on gonality relative to genus.

Contribution

It extends the validity of the Green-Lazarsfeld gonality conjecture to a broader class of generic curves with specific gonality bounds.

Findings

The conjecture holds for generic curves with genus g and gonality d when g/3<d<[g/2]+2.

Uses Green's canonical syzygy conjecture as a key tool.

Provides new bounds linking gonality and genus for generic curves.

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 $g/3<d<[g/2]+2$.