Holomorphic rank of hypersurfaces with an isolated singularity

LetV be a germ at 0 C ²,n3, of hypersurface with an isolated singularity at 0. In this paper we prove that the maximal number of germs of vector fields inV ^*=V–0, which are linearly independent in all points ofV ^* is two. In the casesn=3,4 and of quasi homogeneous hypersurfaces (n3), we prove that this number is one.Dedicated to the memory of R. MañéThis research was partially supported by Pronex.