Mathematical Research Letters

Volume 4 (1997)

Number 6

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

Pages: 823 – 842



Dmitri Zaitsev (Universität Tübingen)


The topic of the paper is the study of germs of local holomorphisms $f$ between ${\Bbb C}^n$ and ${\Bbb C}^{n'}$ such that $f(M)\subset M'$ and $df(T^cM)=T^cM'$ for $M\subset {\Bbb C}^n$ and $M'\subset {\Bbb C}^{n'}$ 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.

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