Lipschitz geometry of complex surfaces: analytic invariants and equisingularity

Autor:	Neumann, Walter D., Pichon, Anne
Rok vydání:	2012
Předmět:	Mathematics - Algebraic Geometry Mathematics - Complex Variables 32S15 32S25 32S50 14B07
Druh dokumentu:	Working Paper
Popis:	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. Comment: Added a new section 10 to correct a minor gap and simplify some arguments
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1211.4897 Zobrazit plný text záznamu View this record from Arxiv