Explicit Kummer surface formulas for arbitrary characteristic

Abstract

AbstractIfCis a curve of genus 2 defined over a fieldkandJis its Jacobian, then we can associate a hypersurfaceKin3toJ, called the Kummer surface ofJ. Flynn has made this construction explicit in the case when the characteristic ofkis not 2 andCis given by a simplified equation. He has also given explicit versions of several maps defined on the Kummer surface and shown how to perform arithmetic onJusing these maps. In this paper we generalize these results to the case of arbitrary characteristic.