The group law on the jacobian of a curve of genus 2

Abstract

An explicit description is given of the group law on the Jacobian of a curve C of genus 2. The Kummer surface provides a useful intermediary stage; bilinear forms relating to the Kummer surface imply that the global group law may be given projectively by biquadratic forms defined over the same ring as the coefficients of C. It is not assumed that C has a rational Weierstrass point, and the theory presented applies over an arbitrary ground field.