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Explicit Kummer varieties of hyperelliptic Jacobian threefolds

  • J. Steffen Müller (a1)
Abstract
Abstract

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.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

C. Birkenhake and H. Lange , Complex Abelian varieties, 2nd edn (Springer, Berlin, 2004).

D. Holmes , ‘Computing Néron–Tate heights of points on hyperelliptic Jacobians’, J. Number Theory 132 (2012) no. 2, 12951305.

J. S. Müller , ‘Computing canonical heights using arithmetic intersection theory’, Math. Comput. 83 (2014) 311336.

D. Mumford , ‘On the equations defining abelian varieties. I’, Invent. Math. 1 (1966) 287354.

M. Stoll , ‘On the height constant for curves of genus two, II’, Acta Arith. 104 (2002) 165182.

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LMS Journal of Computation and Mathematics
  • ISSN: -
  • EISSN: 1461-1570
  • URL: /core/journals/lms-journal-of-computation-and-mathematics
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