Some equations for the universal Kummer variety

Abstract

We give a method to find quartic equations for Kummer varieties and we give some explicit examples. From these equations for g g -dimensional Kummer varieties one obtains equations for the moduli space of g + 1 g+1 -dimensional Kummer varieties. These again define modular forms which vanish on the period matrices of Riemann surfaces. The modular forms that we find for g = 5 g=5 appear to be new and of lower weight than known before.