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Explicit Kummer surface formulas for arbitrary characteristic

Part of: Computational aspects in algebraic geometry Arithmetic algebraic geometry Finite fields and commutative rings (number-theoretic aspects) Curves Surfaces and higher-dimensional varieties

Published online by Cambridge University Press:  01 January 2010

Jan Steffen Müller
Jan Steffen Müller*
Affiliation:
Department of Mathematics, University of Bayreuth, 95440 Bayreuth, Germany (email: [email protected])

Abstract

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If C is a curve of genus 2 defined over a field k and J is its Jacobian, then we can associate a hypersurface K in ℙ3 to J, called the Kummer surface of J. Flynn has made this construction explicit in the case when the characteristic of k is not 2 and C is given by a simplified equation. He has also given explicit versions of several maps defined on the Kummer surface and shown how to perform arithmetic on J using these maps. In this paper we generalize these results to the case of arbitrary characteristic.

MSC classification

Secondary: 14J28: $K3$ surfaces and Enriques surfaces 14H40: Jacobians, Prym varieties 14Q10: Surfaces, hypersurfaces 11T71: Algebraic coding theory; cryptography 11G50: Heights
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 13 , January 2010 , pp. 47 - 64
Copyright
Copyright © London Mathematical Society 2010

References

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Supplementary material: File

Müller supplementary material

Formulae appendix

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