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arXiv · 1211.4897

Lipschitz geometry of complex surfaces: analytic invariants and equisingularity

Walter D. Neumann·Anne Pichon
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Abstract

We prove that the outer Lipschitz geometry of a germ $(X,0)$ of a normal complex surface singularity determines a large amount of its analytic structure. In particular, it follows that any analytic family of normal surface singularities with constant Lipschitz geometry is Zariski equisingular. We also prove a strong converse for families of normal complex hypersurface singularities in $\mathbb C^3$: Zariski equisingularity implies Lipschitz triviality. So for such a family Lipschitz triviality, constant Lipschitz geometry and Zariski equisingularity are equivalent to each other.

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Walter D. Neumann, Anne Pichon. 2012-11-20. Lipschitz geometry of complex surfaces: analytic invariants and equisingularity. https://arxiv.org/abs/1211.4897

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