Explicit Kummer surface theory for arbitrary characteristic
Algebraic Geometry
2014-01-28 v1 Number Theory
Abstract
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.
Cite
@article{arxiv.0910.2589,
title = {Explicit Kummer surface theory for arbitrary characteristic},
author = {Jan Steffen Müller},
journal= {arXiv preprint arXiv:0910.2589},
year = {2014}
}
Comments
To be published in the LMS Journal of Computation and Mathematics