Explicit Kummer surface theory for arbitrary characteristic

Details Explicit Kummer surface theory for arbitrary characteristic Explicit Kummer surface theory for arbitrary characteristic

2009-10-14

arxiv.org/abs/0910.2589v1

London Math. Soc. J. Comput. Math., volume 13, pp. 47-64 (2010)

Mathematics

Algebraic Geometry

To be published in the LMS Journal of Computation and Mathematics

Scientific paper

We explicitly find an equation and a projective embedding of the Kummer surface associated to the Jacobian of a curve of genus 2 given by an equation of the form y^2 + h(x)y = f(x) over an arbitrary ground field as well as several maps that can be used to perform arithmetic on it. This extends earlier work by Flynn and has applications, for instance, in computations of canonical heights for genus 2 Jacobians and in cryptography.

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