Universal abelian covers of certain surface singularities |
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Authors: | Tomohiro Okuma |
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Institution: | (1) Department of Education, Yamagata University, 1-4-12 Kojirakawa-machi, Yamagata 990-8560, Japan |
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Abstract: | Every normal complex surface singularity with -homology sphere link has a universal abelian cover. It has been conjectured by Neumann and Wahl that the universal abelian
cover of a rational or minimally elliptic singularity is a complete intersection singularity defined by a system of ``splice
diagram equations'. In this paper we introduce a Neumann-Wahl system, which is an analogue of the system of splice diagram
equations, and prove the following.
If (X, o) is a rational or minimally elliptic singularity, then its universal abelian cover (Y, o) is an equisingular deformation of an isolated complete intersection singularity (Y0, o) defined by a Neumann-Wahl system. Furthermore, if G denotes the Galois group of the covering Y → X, then G also acts on Y0 and X is an equisingular deformation of the quotient Y0/G.
Dedicated to Professor Jonathan Wahl on his sixtieth birthday.
This research was partially supported by the Grant-in-Aid for Young Scientists (B), The Ministry of Education, Culture, Sports,
Science and Technology, Japan. |
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Keywords: | 32S25 14B05 14J17 |
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