manuscripta mathematica

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

On the classification of Hilbert modular threefolds

  • H. G. Grundman


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.


General Type Number Field Arithmetic Genus Kodaira Dimension Real Number Field 
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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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