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Pré-Publication, Document De Travail Année : 2012

Lipschitz geometry of complex surfaces: analytic invariants and equisingularity

Résumé

We prove that the outer Lipschitz geometry of the germ 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 $\C^3$: 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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Dates et versions

hal-01130560 , version 1 (12-03-2015)

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  • HAL Id : hal-01130560 , version 1

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Walter D Neumann, Anne Pichon. Lipschitz geometry of complex surfaces: analytic invariants and equisingularity. 2012. ⟨hal-01130560⟩
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