Difference varieties and the Green-Lazarsfeld Secant Conjecture
Algebraic Geometry
2026-05-27 v2 Commutative Algebra
Abstract
The Green-Lazarsfeld Secant Conjecture is a generalization of Green's Conjecture on syzygies of canonical curves to the cases of arbitrary line bundles. We establish the Green-Lazarsfeld Secant Conjecture for curves of genus g in all the divisorial case, that is, when the line bundles that fail to be (p+1)-very ample form a divisor in the Jacobian of the curve.
Cite
@article{arxiv.2307.14157,
title = {Difference varieties and the Green-Lazarsfeld Secant Conjecture},
author = {Gavril Farkas},
journal= {arXiv preprint arXiv:2307.14157},
year = {2026}
}
Comments
12 pages. Final version, to appear in the Epiga volume dedicated to Claire Voisin