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

1998/01/09 by Dmitri Zaitsev, Zaitsev, Dmitri
Mathematics · #32C16 #32D15 #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Meromorphic and Entire Functions #math.CV #msc:32C16 #msc:32D15

paper · pdf · doi:10.48550/arxiv.math/9801041

17 pages

arxiv created 1998/01/09 · openalex publication_date 1998/01/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The topic of the paper is the study of germs of local holomorphisms f between Cⁿ and C^n' such that f(M)⊂ M' and df(T^cM)=T^cM' for M⊂ Cⁿ and M'⊂ 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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