Separating sets, metric tangent cone and applications for complex algebraic germs

Details Separating sets, metric tangent cone and applications for complex algebraic germs Separating sets, metric tangent cone and applications for complex algebraic germs

2009-05-27

arxiv.org/abs/0905.4312v1

Selecta Math. 16 (2010), 377-391

Mathematics

Algebraic Geometry

12 pages. This paper includes the results of arXiv:0809.0845

Scientific paper

10.1007/s00029-010-0024-0

An explanation is given for the initially surprising ubiquity of separating sets in normal complex surface germs. It is shown that they are quite common in higher dimensions too. The relationship between separating sets and the geometry of the metric tangent cone of Bernig and Lytchak is described. Moreover, separating sets are used to show that the inner Lipschitz type need not be constant in a family of normal complex surface germs of constant topology.

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