中文

Complete intersection singularities of splice type as universal abelian covers

代数几何 2014-11-11 v2 几何拓扑

摘要

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.

关键词

引用

@article{arxiv.math/0407287,
  title  = {Complete intersection singularities of splice type as universal abelian covers},
  author = {Walter D Neumann and Jonathan Wahl},
  journal= {arXiv preprint arXiv:math/0407287},
  year   = {2014}
}

备注

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