Brill-Noether theory and Green's conjecture for general curves on simple abelian surfaces

Federico Moretti

Brill-Noether theory and Green's conjecture for general curves on simple abelian surfaces

Algebraic Geometry 2025-03-25 v4

Authors: Federico Moretti

Abstract

In this paper we compute the gonality and the dimension of the Brill-Noether loci $W^1_d(C)$ for curves in a non primitive linear system of a simple abelian surface, adapting vector bundles techniques \`a la Lazarsfeld originally introduced with $K3$ surfaces. As a corollary, we obtain general Green's conjecture for curves on abelian surfaces.

Keywords

Brill-Noether theory Green's conjecture abelian surfaces vector bundles gonality linear systems

Cite

@article{arxiv.2205.15977,
  title  = {Brill-Noether theory and Green's conjecture for general curves on simple abelian surfaces},
  author = {Federico Moretti},
  journal= {arXiv preprint arXiv:2205.15977},
  year   = {2025}
}

Comments

Accepted version, exposition improved following referee reports and small change in the statement of Theorem 1.5. To appear in IMRN

Brill-Noether theory and Green's conjecture for general curves on simple abelian surfaces

Abstract

Keywords

Cite

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