Displaying similar documents to “Cartan-Chern-Moser theory on algebraic hypersurfaces and an application to the study of automorphism groups of algebraic domains”

On the mapping problem for algebraic real hypersurfaces in the complex spaces of different dimensions

Xiaojun Huang (1994)

Annales de l'institut Fourier

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In this paper, we show that if M 1 and M 2 are algebraic real hypersurfaces in (possibly different) complex spaces of dimension at least two and if f is a holomorphic mapping defined near a neighborhood of M 1 so that f ( M 1 ) ⊂ M 2 , then f is also algebraic. Our proof is based on a careful analysis on the invariant varieties and reduces to the consideration of many cases. After a slight modification, the argument is also used to prove a reflection principle, which allows our main result to be stated for...

Germs of holomorphic mappings between real algebraic hypersurfaces

Nordine Mir (1998)

Annales de l'institut Fourier

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We study germs of holomorphic mappings between general algebraic hypersurfaces. Our main result is the following. If ( M , p 0 ) and ( M ' , p 0 ' ) are two germs of real algebraic hypersurfaces in ℂ N + 1 , N ≥ 1 , M is not Levi-flat and H is a germ at p 0 of a holomorphic mapping such that H ( M ) ⊆ M ' and Jac ( H ) ≢ 0 then the so-called reflection function associated to H is always holomorphic algebraic. As a consequence, we obtain that if M ' is given in the so-called normal form, the transversal component of H is always algebraic. Another...

On algebraic solutions of algebraic Pfaff equations

Henryk Żołądek (1995)

Studia Mathematica

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We give a new proof of Jouanolou’s theorem about non-existence of algebraic solutions to the system ẋ = z s , ẏ = x s , ż = y s . We also present some generalizations of the results of Darboux and Jouanolou about algebraic Pfaff forms with algebraic solutions.