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Hyperelliptic genus 4 curves on abelian surfaces


Authors: Paweł Borówka and G. K. Sankaran
Journal: Proc. Amer. Math. Soc. 145 (2017), 5023-5034
MSC (2010): Primary 14K10; Secondary 14H42
DOI: https://doi.org/10.1090/proc/13795
Published electronically: August 31, 2017
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Abstract: We study smooth curves on abelian surfaces, especially for genus $ 4$, when the complementary subvariety in the Jacobian is also a surface. We show that up to translation there is exactly one genus $ 4$ hyperelliptic curve on a general $ (1,3)$-polarised abelian surface. We investigate these curves and show that their Jacobians contain a surface and its dual as complementary abelian subvarieties.


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Paweł Borówka
Affiliation: Institute of Mathematics, Jagiellonian University in Kraków, ul. prof Stanisława Łojasiewicza 6, 30-348 Kraków, Poland
Email: Pawel.Borowka@uj.edu.pl

G. K. Sankaran
Affiliation: Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, England
Email: G.K.Sankaran@bath.ac.uk

DOI: https://doi.org/10.1090/proc/13795
Received by editor(s): July 21, 2016
Published electronically: August 31, 2017
Communicated by: Lev Borisov
Article copyright: © Copyright 2017 American Mathematical Society

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