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Families of abelian surfaces with real multiplication over Hilbert modular surfaces

Published online by Cambridge University Press:  22 January 2016

G. van der Geer  and
K. Ueno
G. van der Geer
Affiliation:
University of Amsterdam, Kyoto University
K. Ueno
Affiliation:
University of Amsterdam, Kyoto University
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Around the beginning of this century G. Humbert ([9]) made a detailed study of the properties of compact complex surfaces which can be parametrized by singular abelian functions. A surface parametrized by singular abelian functions is the image under a holomorphic map of a singular abelian surface (i.e. an abelian surface whose endomorphism ring is larger than the ring of rational integers). Humbert showed that the periods of a singular abelian surface satisfy a quadratic relation with integral coefficients and he constructed an invariant D of such a relation with respect to the action of the integral symplectic group on the periods.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 88 , December 1982 , pp. 17 - 53
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1982

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