Complete intersection singularities of splice type as universal abelian covers

Abstract

It has long been known that every quasi-homogeneous normal complex surface singularity with Q-homology sphere link has universal abelian cover a Brieskorn complete intersection singularity. We describe a broad generalization: First, one has a class of complete intersection normal complex surface singularities called "splice type singularities", which generalize Brieskorn complete intersections. Second, these arise as universal abelian covers of a class of normal surface singularities with Q-homology sphere links, called "splice-quotient singularities". According to the Main Theorem, splice-quotients realize a large portion of the possible topologies of singularities with Q-homology sphere links. As quotients of complete intersections, they are necessarily Q-Gorenstein, and many Q-Gorenstein singularities with Q-homology sphere links are of this type. We conjecture that rational singularities and minimally elliptic singularities with Q-homology sphere links are splice-quotients. A recent preprint of T Okuma presents confirmation of this conjecture.

Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol9/paper17.abs.html

References in corpus (4)

• Rational singularities
• Complex surface singularities with integral homology sphere links
• Universal abelian covers of certain surface singularities
• Links and analytic invariants of superisolated singularities

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• Complex analytic realization of links
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