  We prove the existence (and give a characterization) of a germ of complex
analytic set left invariant by an abelian group of germs of holomorphic
diffeomorphisms at a common fixed point.We also give condition that ensure that
such a group can be linearized holomorphically near the fixed point. It rests
on a "small divisors condition" of the family of linear parts. The second part
of this article is devoted to the study families of totally real intersecting
n-submanifolds of (C n , 0). We give some conditions which allow to straighten
holomorphically the family. If this is not possible to do it formally, we
construct a germ of complex analytic set at the origin which interesection with
the family can be holomorphically straightened. The second part is an
application of the first.
