Green's Conjecture for the generic canonical curve

TL;DR

This paper proves Green's Conjecture for the generic canonical curve, establishing a key link between syzygies and Clifford index for most curves of a given genus.

Contribution

It provides a proof that the generic curve of any genus g satisfies Green's Conjecture, confirming a long-standing hypothesis in algebraic geometry.

Findings

Green's Conjecture holds for generic canonical curves of any genus

Syzygies of the canonical model are simple up to the p-th stage based on Clifford index

The result confirms the conjecture for a broad class of algebraic curves

Abstract

Green's Conjecture states the following : syzygies of the canonical model of a curve are simple up to the p^th stage if and only if the Clifford index of C is greater than p. We prove that the generic curve of genus g satisfies Green's conjecture.