On the partial algebraicity of holomorphic mappings between two real algebraic sets

Joël Merker

Displaying similar documents to “On the partial algebraicity of holomorphic mappings between two real algebraic sets”

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 $ℂ^{N + 1}$ , $N \geq 1$ , $M$ is not Levi-flat and $H$ is a germ at $p_{0}$ of a holomorphic mapping such that $H (M) \subseteq M^{'}$ 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 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 $f (M_{1}) \subset M_{2}$ , 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...

Holomorphic mappings between algebraic hypersurfaces in complex space

M. S. Baouendi, L. P. Rothschild (1994-1995)

Séminaire Équations aux dérivées partielles (Polytechnique)

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The theorem of Forelli for holomorphic mappings into complex spaces

Pham Ngoc Mai, Do Duc Thai, Le Tai Thu (2004)

Annales Polonici Mathematici

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Generalizations of the theorem of Forelli to holomorphic mappings into complex spaces are given.

Proper holomorphic self-mappings of the symmetrized bidisc

Armen Edigarian (2004)

Annales Polonici Mathematici

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We characterize proper holomorphic self-mappings 𝔾₂ → 𝔾₂ for the symmetrized bidisc 𝔾₂ = {(λ₁+λ₂,λ₁λ₂): |λ₁|,|λ₂| < 1} ⊂ ℂ².

The Łojasiewicz exponent of c-holomorphic mappings

Maciej P. Denkowski (2005)

Annales Polonici Mathematici

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The aim of this paper is to study the Łojasiewicz exponent of c-holomorphic mappings. After introducing an order of flatness for c-holomorphic mappings we give an estimate of the Łojasiewicz exponent in the case of isolated zero, which is a generalization of the one given by Płoski and earlier by Chądzyński for two variables.

Recent developments in the theory of separately holomorphic mappings

Viêt-Anh Nguyên (2009)

Colloquium Mathematicae

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We describe a part of the recent developments in the theory of separately holomorphic mappings between complex analytic spaces. Our description focuses on works using the technique of holomorphic discs.

A uniqueness theorem of Cartan-Gutzmer type for holomorphic mappings in ℂⁿ

Piotr Liczberski, Jerzy Połubiński (2002)

Annales Polonici Mathematici

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We continue our previous work on a problem of Janiec connected with a uniqueness theorem, of Cartan-Gutzmer type, for holomorphic mappings in ℂⁿ. To solve this problem we apply properties of (j;k)-symmetrical functions.

On fixed points of holomorphic type

Ewa Ligocka (2002)

Colloquium Mathematicae

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We study a linearization of a real-analytic plane map in the neighborhood of its fixed point of holomorphic type. We prove a generalization of the classical Koenig theorem. To do that, we use the well known results concerning the local dynamics of holomorphic mappings in ℂ².

The range of vector valued holomorphic mappings

Richard M. Aron (1976)

Annales Polonici Mathematici

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Holomorphic mappings between spaces of different dimensions. I.

Peichu Hu (1993)

Mathematische Zeitschrift

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Holomorphic bijections of algebraic sets

Sławomir Cynk, Kamil Rusek (1997)

Annales Polonici Mathematici

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We prove that every holomorphic bijection of a quasi-projective algebraic set onto itself is a biholomorphism. This solves the problem posed in [CR].

Holomorphic mappings between spaces of different dimensions. II.

Peichu Hu (1994)

Mathematische Zeitschrift

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Extending proper holomorphic mappings of positive codimension.

Franc Forstneric (1989)

Inventiones mathematicae

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A note on the Nullstellensatz for c-holomorphic functions

Maciej P. Denkowski (2007)

Annales Polonici Mathematici

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We begin this article with a graph theorem and a kind of Nullstellensatz for weakly holomorphic functions. This yields a general Nullstellensatz for c-holomorphic functions on locally irreducible sets. In Section 2 some methods of Płoski-Tworzewski permit us to prove an effective Nullstellensatz for c-holomorphic functions in the case of a proper intersection with the degree of the intersection cycle as exponent. We also extend this result to the case of isolated improper intersection,...

Lineability of the set of holomorphic mappings with dense range

Jerónimo López-Salazar (2012)

Studia Mathematica

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Let U be an open subset of a separable Banach space. Let ℱ be the collection of all holomorphic mappings f from the open unit disc 𝔻 ⊂ ℂ into U such that f(𝔻) is dense in U. We prove the lineability and density of ℱ in appropriate spaces for different choices of U.

Proper holomorphic mappings between rigid polynomial domains in C.

Bernard Coupet, Nabil Ourimi (2001)

Publicacions Matemàtiques

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We describe the branch locus of proper holomorphic mappings between rigid polynomial domains in C. It appears, in particular, that it is controlled only by the first domain. As an application, we prove that proper holomorphic self-mappings between such domains are biholomorphic.

Approximation of holomorphic maps by algebraic morphisms

J. Bochnak, W. Kucharz (2003)

Annales Polonici Mathematici

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Let X be a nonsingular complex algebraic curve and let Y be a nonsingular rational complex algebraic surface. Given a compact subset K of X, every holomorphic map from a neighborhood of K in X into Y can be approximated by rational maps from X into Y having no poles in K. If Y is a nonsingular projective complex surface with the first Betti number nonzero, then such an approximation is impossible.