Bi-Lipschitz geometry of weighted homogeneous surface singularities

Birbrair, Lev; Fernandes, Alexandre; Neumann, Walter D.

Bi-Lipschitz geometry of weighted homogeneous surface singularities

Authors

Birbrair, Lev

Fernandes, Alexandre

Neumann, Walter D.

Description

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