Some equations for the universal kummer variety

We give a method to find quartic equations for Kummer varieties and we give some explicit examples. From these equations for gdimensional Kummer varieties one obtains equations for the moduli space of 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 appear to be new and of lower weight than known before.