Hyperelliptic genus 4 curves on abelian surfaces
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- by Paweł Borówka and G. K. Sankaran PDF
- Proc. Amer. Math. Soc. 145 (2017), 5023-5034 Request permission
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.References
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Additional Information
- 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
- Received by editor(s): July 21, 2016
- Published electronically: August 31, 2017
- Communicated by: Lev Borisov
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 5023-5034
- MSC (2010): Primary 14K10; Secondary 14H42
- DOI: https://doi.org/10.1090/proc/13795
- MathSciNet review: 3717933