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The Classification of Hilbert Modular Surfaces

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

Abstract

In the next two chapters the emphasis is on the geometry of Hilbert modular surfaces. Algebraic surfaces are classified by the growth of their plurigenera, which roughly speaking is a way of measuring the ampleness of the canonical divisor class. On Hilbert modular surfaces we have in some sense two “canonical divisor classes”, the usual canonical class c 1 2 ) and the class c 1(Ω 2(logD)) with D the divisor resolving the cusps. The second one is more natural for Hilbert modular surfaces, but by using the first one the standard theory of algebraic surfaces becomes available. Since the difference D of c 1 2 (logD)) and c 1 2 ) is relatively small if the volume of Γ\ℌ 2is big one expects in general that the two classes behave similarly.

Keywords

Blow Down Algebraic Surface Elliptic Surface Irreducible Curve Quotient Singularity 
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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