Brill–Noether Theory and Green’s Conjecture for General Curves on Simple Abelian Surfaces

Federico Moretti

doi:10.1093/imrn/rnaf073

Brill–Noether Theory and Green’s Conjecture for General Curves on Simple Abelian Surfaces

Federico Moretti

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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 Green’s conjecture for general curves on abelian surfaces.

Original language	English
Article number	rnaf073
Journal	International Mathematics Research Notices
Volume	2025
Issue number	7
DOIs	https://doi.org/10.1093/imrn/rnaf073
State	Published - Apr 1 2025

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title = "Brill–Noether Theory and Green{\textquoteright}s Conjecture for General Curves on Simple Abelian Surfaces",

abstract = "We compute the gonality and the dimension of the Brill–Noether loci W1d(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 Green{\textquoteright}s conjecture for general curves on abelian surfaces.",

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N2 - We compute the gonality and the dimension of the Brill–Noether loci W1d(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 Green’s conjecture for general curves on abelian surfaces.

AB - We compute the gonality and the dimension of the Brill–Noether loci W1d(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 Green’s conjecture for general curves on abelian surfaces.

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Brill–Noether Theory and Green’s Conjecture for General Curves on Simple Abelian Surfaces

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