Differential invariance of the multiplicity of real and complex analytic sets

TL;DR

This paper proves that the multiplicity of real and complex analytic sets remains invariant under differential transformations, including a real version of Gau-Lipman's Theorem and its generalization.

Contribution

It establishes the differential invariance of multiplicity for real and complex analytic sets, extending Gau-Lipman's Theorem to the real case and providing a broader generalization.

Findings

Multiplicity mod 2 of real analytic sets is a differential invariant

Proved the real version of Gau-Lipman's Theorem

Generalized Gau-Lipman's Theorem for broader applicability

Abstract

This paper is devoted to proving the differential invariance of the multiplicity of real and complex analytic sets. In particular, we prove the real version of Gau-Lipman's Theorem, i.e., it is proved that the multiplicity mod 2 of real analytic sets is a differential invariant. We prove also a generalization of Gau-Lipman's Theorem.