Resolution of the Cusp Singularities

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


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.


Line Bundle Modular Form Complex Manifold Local Ring Quotient Singularity 
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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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