Abstract
AbstractWe 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.
Subject
Computational Theory and Mathematics,General Mathematics
Reference22 articles.
1. Prolegomena to a Middlebrow Arithmetic of Curves of Genus 2
2. Explicit Kummer surface formulas for arbitrary characteristic
3. 21. M. Stoll , An explicit theory of heights for hyperelliptic Jacobians of genus three, 2014 (in preparation) (See also http://www.mathe2.uni-bayreuth.de/stoll/talks/Luminy2012.pdf.).
4. The Jacobian and formal group of a curve of genus 2 over an arbitrary ground field
5. 22. A. G. J. Stubbs , ‘Hyperelliptic curves’, PhD Thesis, University of Liverpool, 2000.
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