English

Bi-Lipschitz geometry of weighted homogeneous surface singularities

Algebraic Geometry 2008-09-04 v3 Geometric Topology Metric Geometry

Abstract

We show that a weighted homogeneous complex surface singularity is metrically conical (i.e., bi-Lipschitz equivalent to a metric cone) only if its two lowest weights are equal. We also give an example of a pair of weighted homogeneous complex surface singularities that are topologically equivalent but not bi-Lipschitz equivalent.

Keywords

Cite

@article{arxiv.0704.2041,
  title  = {Bi-Lipschitz geometry of weighted homogeneous surface singularities},
  author = {Lev Birbrair and Alexandre Fernandes and Walter D. Neumann},
  journal= {arXiv preprint arXiv:0704.2041},
  year   = {2008}
}

Comments

5 pages. Added result that nonhomogeneous cyclic quotients are not conical