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

2022/05/31 by Federico Moretti, Moretti, Federico
Mathematics · #14H51 #14J60 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.2205.15977

openalex publication_date 2022/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we compute the gonality and the dimension of the Brill-Noether loci W¹_d(C) for curves in a non primitive linear system of a simple abelian surface, adapting vector bundles techniques à la Lazarsfeld originally introduced with K3 surfaces. As a corollary, we obtain general Green's conjecture for curves on abelian surfaces.

Related

• Brill-Noether theory for curves on generic abelian surfaces
• Brill--Noether loci in genus ≤ 12
• Severi Varieties and Brill-Noether theory of curves on abelian surfaces
• Non-Abelian Brill-Noether theory and Fano 3-folds
• Mukai's program for non-primitive curves on K3 surfaces