Extending holomorphic mappings from subvarieties in Stein manifolds

[Prolongements holomorphes dans les variétés de Stein]

Forstneric, Franc

Annales de l'Institut Fourier, Tome 55 (2005), p. 733-751 / Harvested from Numdam

Résumé

Soit $Y$ une variété analytique complexe telle que toute application holomorphe d’une partie convexe compacte de l’espace euclidien ${\mathbb {C}}^n$ à valeurs dans $Y$ est limite uniforme d’applications entières à valeurs dans $Y$. On prouve que toute application holomorphe d’un sous ensemble analytique complexe fermé $X_0$ d’une variété de Stein $X$ à valeurs dans $Y$ possède un prolongement holomorphe à $X$ à condition qu’elle admette un prolongement continu. On établit ensuite l’équivalence entre quatre propriétés de type Oka pour une variété analytique complexe.

Abstract

Suppose that $Y$ is a complex manifold such that any holomorphic map from a compact convex set in a Euclidean space ${\mathbb {C}}^n$ to $Y$ is a uniform limit of entire maps ${\mathbb {C}}^n\rightarrow Y$. We prove that a holomorphic map $X_0 \rightarrow Y$ from a closed complex subvariety $X_0$ in a Stein manifold $X$ admits a holomorphic extension $X\rightarrow Y$ provided that it admits a continuous extension. We then establish the equivalence of four Oka-type properties of a complex manifold.

Détail

Publié le : 2005-01-01

MR 2149401 | Zbl 1076.32003 | 1 citation dans Numdam

DOI : https://doi.org/10.5802/aif.2112
Classification:  32E10,  32E30,  32H02
Mots clés: variétés de Stein, applications holomorphes, propriété d'Oka

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