Explicit Kummer surface theory for arbitrary characteristic
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 y2 + 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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