On the Link Space of a ℚ-Gorenstein Quasi-Homogeneous Surface Singularity

  • Anna Pratoussevitch
Conference paper
Part of the Trends in Mathematics book series (TM)


In this paper we prove the following theorem: Let M be the link space of a quasi-homogeneous hyperbolic ℚ-Gorenstein surface singularity. Then M is diffeomorphic to a coset space \( \tilde \Gamma _1 \backslash \tilde G/\tilde \Gamma _2 \), where \( \tilde G \) is the 3-dimensional Lie group \( \widetilde{PSL}(2,\mathbb{R}) \), while \( \tilde \Gamma _1 \) and \( \tilde \Gamma _2 \) are discrete subgroups of \( \tilde G \), the subgroup \( \tilde \Gamma _1 \) is co-compact and \( \tilde \Gamma _2 \) is cyclic. Conversely, if M is diffeomorphic to a coset space as above, then M is diffeomorphic to the link space of a quasi-homogeneous hyperbolic ℚ-Gorenstein singularity. We also prove the following characterisation of quasi-homogeneous ℚ-Gorenstein surface singularities: A quasi-homogeneous surface singularity is ℚ-Gorenstein of index r if and only if for the corresponding automorphy factor (U, Γ, L) some tensor power of the complex line bundle L is Γ-equivariantly isomorphic to the rth tensor power of the tangent bundle of the Riemannian surface U.


ℚ-Gorenstein singularity quasi-homogeneous singularity 


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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2006

Authors and Affiliations

  • Anna Pratoussevitch
    • 1
  1. 1.Mathematisches InstitutUniversität BonnBonnGermany

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