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Complete intersection
singularities of splice type as universal abelian covers
Walter D Neumann and Jonathan Wahl |
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Geometry & Topology 9 (2005) 699–755
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arXiv: math.AG/0407287 |
Abstract |
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It has long been known that every quasi-homogeneous normal complex surface singularity with –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 –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 –homology sphere links. As quotients of complete intersections, they are necessarily –Gorenstein, and many –Gorenstein singularities with –homology sphere links are of this type. We conjecture that rational singularities and minimally elliptic singularities with –homology sphere links are splice-quotients. A recent preprint of T Okuma presents confirmation of this conjecture. |
Keywords
surface singularity, Gorenstein singularity, rational
homology sphere, complete intersection singularity, abelian
cover
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Mathematical Subject Classification 2000
Primary: 32S50, 14B05
Secondary: 57M25, 57N10
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References |
Forward citations |
Publication
Received: 31 October 2004
Revised: 18 April 2005
Accepted: 6 March 2005
Published: 28 April 2005
Proposed: Robion Kirby
Seconded: Ronald Fintushel, Ronald Stern
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Authors |
| Walter D Neumann | |
| Department of Mathematics Barnard College Columbia University New York New York 10027 USA |
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| Jonathan Wahl | |
| Department of Mathematics The University of North Carolina Chapel Hill North Carolina 27599-3250 USA |
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