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Explicit Kummer varieties of hyperelliptic Jacobian threefolds

Part of: Arithmetic algebraic geometry Surfaces and higher-dimensional varieties Abelian varieties and schemes

Published online by Cambridge University Press:  01 September 2014

J. Steffen Müller
J. Steffen Müller*
Affiliation:
Institut für Mathematik, Carl von Ossietzky Universität Oldenburg, 26111 Oldenburg, Germany email jan.steffen.mueller@uni-oldenburg.de

Abstract

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We explicitly construct the Kummer variety associated to the Jacobian of a hyperelliptic curve of genus 3 that is defined over a field of characteristic not equal to 2 and has a rational Weierstrass point defined over the same field. We also construct homogeneous quartic polynomials on the Kummer variety and show that they represent the duplication map using results of Stoll.

Supplementary materials are available with this article.

MSC classification

Secondary: 14K05: Algebraic theory 14J30: $3$-folds 11G10: Abelian varieties of dimension $> 1$ 11G50: Heights
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 17 , Issue 1 , 2014 , pp. 496 - 508
Copyright
© The Author 2014 

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Supplementary material: File

Müller Supplementary Material

Supplementary Material

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