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Brill-Noether theory for curves on generic Abelian surfaces
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Bayer, Arend and Li, Chunyi (2018) Brill-Noether theory for curves on generic Abelian surfaces. Pure and Applied Mathematics Quarterly, 13 (1). pp. 49-76. doi:10.4310/PAMQ.2017.v13.n1.a2 ISSN 1558-8599.
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Official URL: http://dx.doi.org/10.4310/PAMQ.2017.v13.n1.a2
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 Vrd(|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.
Item Type: | Journal Article | ||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
Library of Congress Subject Headings (LCSH): | Abelian groups, Curves, Algebraic | ||||||||
Journal or Publication Title: | Pure and Applied Mathematics Quarterly | ||||||||
Publisher: | International Press | ||||||||
ISSN: | 1558-8599 | ||||||||
Official Date: | 14 September 2018 | ||||||||
Dates: |
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Volume: | 13 | ||||||||
Number: | 1 | ||||||||
Page Range: | pp. 49-76 | ||||||||
DOI: | 10.4310/PAMQ.2017.v13.n1.a2 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Date of first compliant deposit: | 17 May 2018 | ||||||||
Date of first compliant Open Access: | 15 April 2019 | ||||||||
RIOXX Funder/Project Grant: |
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