Lipschitz regular complex algebraic sets are smooth

Les ensembles algébriques complexes Lipschitz réguliers sont lisses

Lev Birbrair (1) , Alexandre Fernandes (1) , Dung Trang Lê (2) , Edson Sampaio (1)

1 UFC - Universidade Federal do Ceará = Federal University of Ceará
2 LATP - Laboratoire d'Analyse, Topologie, Probabilités

A classical Theorem of Mumford implies that a topologically regular complex algebraic surface in C 3 with an isolated singular point is smooth. We prove that any Lipschitz regular complex algebraic set is smooth. No restriction on the dimension and no restriction on the singularity to be isolated is needed.

Mots clés: Lipschitz homeomorphism

Mots clés: Ensembles algébriques complexes

Domaines: Géométrie algébrique [math.AG]; Algèbre commutative [math.AC]; Variables complexes [math.CV]

Lev Birbrair, Alexandre Fernandes, Dung Trang Lê, Edson Sampaio. Lipschitz regular complex algebraic sets are smooth. Proceedings of the American Mathematical Society, 2016, 144, pp.983-987. ⟨10.1090/proc/12783⟩. ⟨hal-01272390⟩