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manuscripta mathematica

, Volume 72, Issue 1, pp 297–305 | Cite as

On the classification of Hilbert modular threefolds

  • H. G. Grundman
Article

Abstract

Letk be a totally real number field with ring of integersO k . The Hilbert modular variety overk is a desingularization of the (natural) compactification of PSL2(O k )∖H k . The purpose of this paper is to present specific numerical bounds on the size of the discriminantd k of a cubic fieldk with Hilbert modular variety of particular classifications. specifically, it is shown that ifd k>2.12×107, then the Hilbert modular variety overk is not rational and further, ifd k>2.77×108, then Hilbert modular variety overk is of general type.

Keywords

General Type Number Field Arithmetic Genus Kodaira Dimension Real Number Field 
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 1991

Authors and Affiliations

  • H. G. Grundman
    • 1
  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridge

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