Explicit Kummer varieties of hyperelliptic Jacobian threefolds

J. Steffen Müller
2014 LMS Journal of Computation and Mathematics  
AbstractWe explicitly construct the Kummer variety associated to the Jacobian of a hyperelliptic curve of genus 3 that is defined over a field of characteristic not equal to 2 and has a rational Weierstrass point defined over the same field. We also construct homogeneous quartic polynomials on the Kummer variety and show that they represent the duplication map using results of Stoll.Supplementary materials are available with this article.
doi:10.1112/s1461157014000126 fatcat:3xwplcawyvh5bnyxg5q6yac2zu