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Brill-Noether theory for curves on generic abelian surfaces

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https://arxiv.org/abs/1603.09218
Original languageEnglish
Pages (from-to)49-76
Number of pages22
JournalPure and applied mathematics quarterly
Volume13
Issue number1
DOIs
Publication statusPublished - 14 Sep 2018

Abstract

We completely describe the Brill-Noether theory for curves in the primitive linear system on generic abelian surfaces, in the following sense: given integers d and r, consider the variety V r d (|H|) parametrizing curves C in the primitive linear system |H| together with a torsion-free sheaf on C of degree d and r+1 global sections. We give a necessary and sufficient condition for this variety to be non-empty, and show that it is either a disjoint union of Grassmannians, or irreducible. Moreover, we show that, when non-empty, it is of expected dimension.
This completes prior results by Knutsen, Lelli-Chiesa and Mongardi.

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