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On the versal deformation of cyclic quotient singularities

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Book cover Singularity Theory and its Applications

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1462))

Abstract

In this paper we prove that the reduced base space of the versal deformation of a cyclic quotient singularity of embedding dimension e has at most irreducible components. All these components are smooth. The components are parametrised by certain continued fractions (introduced by Jan Christophersen), which represent zero. To prove our result, we determine all P-resolutions [K-S-B] by an inductive procedure parallel to the inductive generation of Christophersen's continued fractions. Smoothness of the components is deduced from an explicit description of the infinitesimal deformations of P-resolutions.

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Authors and Affiliations

  1. Mathematisches Seminar der Universität Hamburg, Bundesstraße 55, 2000, Hamburg 13, Federal Republic of Germany

    Jan Stevens

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  1. Jan Stevens
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David Mond James Montaldi

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© 1991 Springer-Verlag Berlin Heidelberg

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Stevens, J. (1991). On the versal deformation of cyclic quotient singularities. In: Mond, D., Montaldi, J. (eds) Singularity Theory and its Applications. Lecture Notes in Mathematics, vol 1462. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086390

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  • DOI: https://doi.org/10.1007/BFb0086390

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53737-3

  • Online ISBN: 978-3-540-47060-1

  • eBook Packages: Springer Book Archive

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