Lipschitz geometry of complex surfaces: analytic invariants and equisingularity

Walter D Neumann (1) , Anne Pichon (2)

1 Columbia University [New York]
2 I2M - Institut de Mathématiques de Marseille

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.

Mots clés: normal surface singularity; Lipschitz geometry; bilipschitz; Zariski equisingularity; Lipschitz equisingularity.

Domaines: Géométrie algébrique [math.AG]

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