Explicit Kummer surface formulas for arbitrary characteristic

Titelangaben

Müller, Jan Steffen:
Explicit Kummer surface formulas for arbitrary characteristic.
In: LMS Journal of Computation and Mathematics. Bd. 13 (2010) . - S. 47-64.
ISSN 1461-1570
DOI: https://doi.org/10.1112/S1461157008000156

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Abstract

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.