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.
Some equations for the universal kummer variety / B. van Geemen. - In: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9947. - 368:1(2016), pp. 209-225. [10.1090/tran/6309]
Some equations for the universal kummer variety
B. van Geemen
2016
Abstract
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.
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