| Résume | Inspired by the work of Pham and Teissier on the Lipschitz saturation of complex analytic varieties, we will use a recent work concerning seminormalization to investigate the Lipschitz saturation of complex algebraic varieties. Similarely to the analytic case, the regular functions of the Lipschitz saturation of a variety correspond to the rational functions that are locally Lipschitz on the closed points of the variety. We focus particularly on the Lipschitz saturation of an algebraic variety into another, and we answer, in this context, to a question of Pham and Teissier regarding the connection between such a construction and normalization. Finally, we will provide algebraic conditions for two varieties to be linked by an algebraic homeomorphism that is locally bi-Lipschitz. |
