Deformations of Surface Singularities pp 229-287

Part of the Bolyai Society Mathematical Studies book series (BSMS, volume 23) | Cite as

Tree Singularities: Limits, Series and Stability

  • Duco Van Straten

Abstract

A tree singularity is a surface singularity that consists of smooth components, glued along smooth curves in the pattern of a tree. Such singularities naturally occur as degenerations of certain rational surface singularities. To be more precise, they can be considered as limits of certain series of rational surface singularities with reduced fundamental cycle. We introduce a general class of limits, construct series deformations for them and prove a stability theorem stating that under the condition of finite dimensionality of T2 the base space of a semi-universal deformation for members high in the series coincides up to smooth factor with the “base space of the limit”. The simplest tree singularities turn out to have already a very rich deformation theory, that is related to problems in plane geometry. From this relation, a very clear topological picture of the Milnor fibre over the different components can be obtained.

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Copyright information

© János Bolyai Mathematical Society and Springer-Verlag 2013

Authors and Affiliations

  • Duco Van Straten
    • 1
  1. 1.Fachbereich Physik, Mathematik und InformatikJohannes Gutenberg-UniversitätMainzGermany

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