#### Geometry & Topology, Vol. 9 (2005)
Paper no. 17, pages 699--755.

## Complete intersection singularities of splice type as universal abelian covers

### Walter D Neumann, Jonathan Wahl

**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.
**Keywords**.
Surface singularity, Gorenstein singularity, rational homology sphere,
complete intersection singularity, abelian cover

**AMS subject classification**.
Primary: 32S50, 14B05.
Secondary: 57M25, 57N10.

**DOI:** 10.2140/gt.2005.9.699

**E-print:** `arXiv:math.AG/0407287`

Submitted to GT on 31 October 2004.
(Revised 18 April 2005.)
Paper accepted 6 March 2005.
Paper published 28 April 2005.

Notes on file formats
Walter D Neumann, Jonathan Wahl

Department of Mathematics, Barnard College, Columbia University

New York,
NY 10027, USA

and

Department of Mathematics, The University of
North Carolina

Chapel Hill, NC 27599-3250, USA

Email: neumann@math.columbia.edu, jmwahl@email.unc.edu

GT home page

## Archival Version

**These pages are not updated anymore.
They reflect the state of
.
For the current production of this journal, please refer to
http://msp.warwick.ac.uk/.
**