Germs of local automorphisms of real analytic CR structures and analytic dependence on the k-jets

Abstract

The topic of the paper is the study of germs of local holomorphisms f between Cn and Cn ? such that f(M)  M? and df(TcM) = TcM? for M  Cn and M?  Cn ? generic real-analytic CR submanifolds of arbitrary codimensions. It is proved that for M minimal and M? finitely nondegenerate, such germs depend analytically on their jets. As a corollary, an analytic structure on the set of all germs of this type is obtained.