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Displaying similar documents to “Infinitesimal CR automorphisms of hypersurfaces of finite type in ℂ 2 ”

Triviality of scalar linear type isotropy subgroup by passing to an alternative canonical form of a hypersurface

Vladimir V. Ežov (1998)

Annales Polonici Mathematici

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The Chern-Moser (CM) normal form of a real hypersurface in ℂ N can be obtained by considering automorphisms whose derivative acts as the identity on the complex tangent space. However, the CM normal form is also invariant under a larger group (pseudo-unitary linear transformations) and it is this property that makes the CM normal form special. Without this additional restriction, various types of normal forms occur. One of them helps to give a simple proof of a (previously complicated)...

On local geometry of finite multitype hypersurfaces

Martin Kolář (2007)

Archivum Mathematicum

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This paper studies local geometry of hypersurfaces of finite multitype. Catlin’s definition of multitype is applied to a general smooth hypersurface in ℂ n + 1 . We prove biholomorphic equivalence of models in dimension three and describe all biholomorphisms between such models. A finite constructive algorithm for computing multitype is described. Analogous results for decoupled hypersurfaces are given.

Low pole order frames on vertical jets of the universal hypersurface

Joël Merker (2009)

Annales de l’institut Fourier

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For low order jets, it is known how to construct meromorphic frames on the space of the so-called vertical k -jets J vert k ( 𝒳 ) of the universal hypersurface 𝒳 ⊂ ℙ n + 1 × ℙ ( n + 1 + d ) ! ( ( n + 1 ) ! d ! ) - 1 parametrizing all projective hypersurfaces X ⊂ ℙ n + 1 ( ℂ ) of degree d . In 2004, for k = n , Siu announced that there exist two constants c n ≥ 1 and c n ′ ≥ 1 such that the twisted tangent bundle T J vert n ( 𝒳 ) ⊗ 𝒪 ℙ n + 1 ( c n ) ⊗ 𝒪 ℙ ( n + 1 + d ) ! ( ( n + 1 ) ! d ! ) - 1 ( c n ′ ) is generated at every point by its global sections. In...

On some rigidity properties of mappings between CR-submanifolds in complex space

Francine Meylan, Nordine Mir, Dimitri Zaitsev (2003)

Journées équations aux dérivées partielles

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We survey some recent results on holomorphic or formal mappings sending real submanifolds in complex space into each other. More specifically, the approximation and convergence properties of formal CR-mappings between real-analytic CR-submanifolds will be discussed, as well as the corresponding questions in the category of real-algebraic CR-submanifolds.