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On Lipschitz normally embedded complex surface germs

Published online by Cambridge University Press:  27 May 2022

André Belotto da Silva
IMJ-PRG, CNRS 7586, Université de Paris, Institut de Mathématiques de Jussieu Paris Rive Gauche, 75013 Paris, France
Lorenzo Fantini
Centre de Mathématiques Laurent Schwartz, Ecole Polytechnique and CNRS, Institut Polytechnique de Paris, 91120 Palaiseau, France
Anne Pichon
Aix Marseille Univ, CNRS, I2M, Marseille, France


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.

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© 2022 The Author(s). The publishing rights in this article are licensed to Foundation Compositio Mathematica under an exclusive licence

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This work is dedicated to Norbert A'Campo


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