Sur l'algébrisabilité locale de sous-variétés analytiques réelles génériques de Cn

We prove that the local (pseudo)group of biholomorphisms stabilizing a minimal, finitely nondegenerate real algebraic submanifold in $\text{C}{}^{\mathrm{n}}$ is a real algebraic local Lie group. We deduce necessary conditions for the local algebraizability of real analytic rigid tubes of arbitrary codimension in $\text{C}{}^{\mathrm{n}}$. To cite this article: H. Gaussier, J. Merker, C. R. Acad. Sci. Paris, Ser. I 336 (2003).