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Humbert Surfaces

  • Gerard van der Geer
Chapter
  • 665 Downloads
Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE3, volume 16)

Abstract

This chapter is devoted to complex abelian surfaces whose endomorphism ring contains an order from a real quadratic field. The moduli spaces of such abelian surfaces are Hilbert modular surfaces. Since the moduli spaces of polarized complex abelian varieties are Siegel modular varieties we find natural maps of Hilbert modular surfaces to Siegel modular threefolds. The images are called Humbert surfaces, after G. Humbert, who studied abelian surfaces with real multiplication, i.e. with an endomorphism ring that contains an order from a real quadratic field.

Keywords

Modulus Space Modular Form Boundary Component Abelian Variety Endomorphism Ring 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Gerard van der Geer
    • 1
  1. 1.Mathematisch InstituutUniversiteit van AmsterdamAmsterdamThe Netherlands

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