Inner Metric Geometry of Complex Algebraic Surfaces with Isolated Singularities
Algebraic Geometry
2007-05-23 v1 Algebraic Topology
Abstract
We produce examples of complex algebraic surfaces with isolated singularities such that these singularities are not metrically conic, i.e. the germs of the surfaces near singular points are not bi-Lipschitz equivalent, with respect to the inner metric, to cones. The technique used to prove the nonexistence of the metric conic structure is related to a development of Metric Homology. The class of the examples is rather large and it includes some surfaces of Brieskorn.
Cite
@article{arxiv.0705.3185,
title = {Inner Metric Geometry of Complex Algebraic Surfaces with Isolated Singularities},
author = {Lev Birbrair and Alexandre Fernandes},
journal= {arXiv preprint arXiv:0705.3185},
year = {2007}
}