Fractions Lipschitziennes d'une algèbre analytique complexe et saturation de Zariski, par Frédéric Pham et Bernard Teissier

Frédéric Pham , Bernard Teissier (1)

1 IMJ - Institut de Mathématiques de Jussieu

Inspired by Zariski's saturation, we associate to each reduced equidimensional germ (X,x) of a complex analytic space the algebra of its meromorphic functions satisfying a Lipschitz condition. We show that it is a local analytic subalgebra of the integral closure of the analytic algebra corresponding to (X,x). In some cases, for example for hypersurfaces, it coincides with Zariski's saturation. Our construction, which relies on the normalized blowing-up of the diagonal in the product XxX, also gives a coordinate-free description of the "transversal" Puiseux characteristic exponents of a plane branch.

Mots clés: Singularités; Puiseux; Lipschitz

Domaines: Variables complexes [math.CV]

Frédéric Pham, Bernard Teissier. Fractions Lipschitziennes d'une algèbre analytique complexe et saturation de Zariski, par Frédéric Pham et Bernard Teissier. 1969. ⟨hal-00384928⟩