Lipschitz fractions of a complex analytic algebra and Zariski saturation

TL;DR

This paper explores the Lipschitz geometry of complex analytic spaces, building on Zariski's saturation theory, and serves as a foundational precursor to modern Lipschitz geometry studies.

Contribution

It introduces a novel perspective linking Zariski's saturation with Lipschitz geometry, providing historical insights and foundational concepts for current research.

Findings

Connects Zariski saturation with Lipschitz geometry

Provides historical context for Lipschitz analysis of complex spaces

Serves as a foundational precursor to modern Lipschitz geometry studies

Abstract

This text is the English translation, due to Naoufal Bouchareb, of an unpublished manuscript of 1969 (the French version is available on HAL as hal-00384928) inspired by Zariski's theory of saturation. Its publication is justified by the fact that it appears now as a precursor of the recently developed study of the Lipschitz geometry (for the outer metric) of germs of complex analytic spaces. This version contains some new footnotes and an additional bibliography.