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Some equations for the universal Kummer variety


Author: Bert van Geemen
Journal: Trans. Amer. Math. Soc. 368 (2016), 209-225
MSC (2010): Primary 14K25; Secondary 14K10
DOI: https://doi.org/10.1090/tran/6309
Published electronically: April 3, 2015
MathSciNet review: 3413861
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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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Additional Information

Bert van Geemen
Affiliation: Dipartimento di Matematica, Università di Milano, Via Saldini 50, 20133 Milano, Italia

DOI: https://doi.org/10.1090/tran/6309
Received by editor(s): October 10, 2013
Received by editor(s) in revised form: October 28, 2013
Published electronically: April 3, 2015
Article copyright: © Copyright 2015 American Mathematical Society