English

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.

Keywords

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

R2 v1 2026-06-21T13:58:08.043Z