Some equations for the universal Kummer variety

van Geemen, Bert

doi:10.1090/tran/6309

Some equations for the universal Kummer variety
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Trans. Amer. Math. Soc. 368 (2016), 209-225 Request permission

Abstract:

We give a method to find quartic equations for Kummer varieties and we give some explicit examples. From these equations for $g$-dimensional 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.

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