Real Algebraic and Analytic Geometry

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207. Lev Birbrair, Alexandre Fernandes:
Metric Geometry of Complex Algebraic Surfaces with Isolated Singularities.

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Submission: 2006, August 11.

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 inner metric, to cones. The technique used to prove the nonexistence of the metric conic structure is related to a development of Metric Homology.

Full text, 11p.: pdf 186k.

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