Universal Abelian Covers of Certain Surface Singularities
نویسنده
چکیده
Every normal complex surface singularity with Q-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.
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