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Resolution of the Cusp Singularities

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

Abstract

In January 1971 Hirzebruch received a letter from Serre in which he was asked whether he knew how to resolve the cusp singularities of Hilbert modular surfaces. Hirzebruch’s answer consisted in a long letter (dated 18 January 1971) in which he explained the resolution process discovered by him just a few days before Serre’s letter arrived. The resolution of cusp singularities is like that of 2-dimensional quotient singularities related to continued fractions, but in contrast to these, the curves occurring in a resolution form a cyclic configuration. By the way, Hirzebruch thus obtained interesting counter examples to a claim made at the end of his own thesis [71] (in which he resolved two-dimensional quotient singularities) saying that such cyclic configurations should not occur.

Keywords

Line Bundle Modular Form Complex Manifold Local Ring 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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