Hyperelliptic genus 4 curves on abelian surfaces

Paweł Borówka; G. K. Sankaran

doi:10.1090/proc/13795

Hyperelliptic genus 4 curves on abelian surfaces

Paweł Borówka, G. K. Sankaran

Jagiellonian University

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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.

Original language	English
Pages (from-to)	5023–5034
Number of pages	12
Journal	Proceedings of the American Mathematical Society
Volume	145
Issue number	12
Early online date	31 Aug 2017
DOIs	https://doi.org/10.1090/proc/13795
Publication status	Published - 1 Dec 2017

Keywords

math.AG
14K05 (Primary) 14K10, 14K25 (Secondary)

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10.1090/proc/13795

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First published in Proceedings of the American Mathematical Society. 145 (2017), published by the American Mathematical Society. © 2017 American Mathematical Society.
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Cite this

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Hyperelliptic genus 4 curves on abelian surfaces

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Gregory Sankaran

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Hyperelliptic genus 4 curves on abelian surfaces

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Gregory Sankaran

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