Singularities of complex algebraic surfaces. Topology and Metric Geometry.

Lev Birbrair.
(Joint work with A. Fernandes and W. Neumann )

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.