On Lipschitz Normally Embedded complex surface germs

Abstract

We undertake a systematic study of Lipschitz Normally Embedded normal complex surface germs. We prove in particular that the topological type of such a germ determines the combinatorics of its minimal resolution which factors through the blowup of its maximal ideal and through its Nash transform, as well as the polar curve and the discriminant curve of a generic plane projection, thus generalizing results of Spivakovsky and Bondil that were known for minimal surface singularities. In an appendix, we give a new example of a Lipschitz Normally Embedded surface singularity.

arXiv commentv4: New appendix with the proof of a folklore result. A few corrections made, exposition improved. 34 pages, 2 figures. To appear in Compositio Mathematica

References in corpus (8)

• The thick-thin decomposition and the bilipschitz classification of normal surface singularities
• Normalized Berkovich spaces and surface singularities
• Minimal surface singularities are Lipschitz normally embedded
• The valuative tree is the projective limit of Eggers-Wall trees
• Inner geometry of complex surfaces: a valuative approach
• Lipschitz normal embedding among superisolated singularities
• A characterization of Lipschitz normally embedded surface singularities
• Moderately Discontinuous Homotopy

Cited by in corpus (2)

• On Lipschitz Normally Embedded singularities
• Polar exploration of complex surface germs