Brill–Noether Theory and Green’s Conjecture for General Curves on Simple Abelian Surfaces
Abstract 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 à la Lazarsfeld originally introduced with $K3$ surfaces. As a corollary, we obtain Green’s conjecture for general curves on abelian surfaces. Dedicated to my Grandparents
Authors
- Federico Moretti (ORCID: https://orcid.org/0000-0001-6561-3279)
Institutions
- Humboldt-Universität zu Berlin (DE)
Publication Details
- Journal
- International Mathematics Research Notices
- Published
- 2025-03-23
- DOI
- https://doi.org/10.1093/imrn/rnaf073
- Primary Topic
- Algebraic Geometry and Number Theory
- Type
- article
- Field-Weighted Citation Impact
- 0.00