Brill-Noether theory and Green's conjecture for general curves on simple abelian surfaces
Abstract
In this paper 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 general Green's conjecture for curves on abelian surfaces.
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