It was shown by Faltings ([Fal84]) and Hriljac ([Hri85]) that the canonical height of a point on the Jacobian of a curve can be expressed as the self intersection of a corresponding divisor on a regular model of the curve. We make this explicit and use it to give an algorithm for computing canonical heights on Jacobians of hyperelliptic curves. To demonstrate the practicality of our algorithm, we illustrate it by computing canonical heights on Jacobians of hyperelliptic curves of genus 1 ≤ g… CONTINUE READING