Lipschitz normal embeddings and polar exploration of complex surface germs

André Belotto da Silva , Lorenzo Fantini , Anne Pichon (1)

1 I2M - Institut de Mathématiques de Marseille

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. This fits in the program of polar explorations, the quest to determine the generic polar variety of a singular surface germ, to which the final part of the paper is devoted. In the appendix, we give a new example of a Lipschitz Normally Embedded surface singularity.

Domaines: Géométrie algébrique [math.AG]

André Belotto da Silva, Lorenzo Fantini, Anne Pichon. Lipschitz normal embeddings and polar exploration of complex surface germs. Compositio Mathematica, In press. ⟨hal-03168406⟩