no. 6
On holomorphic maps into compact non-Kähler manifolds
[Sur les applications holomorphes à valeurs dans variétés compactes non-Kähleriennes]
Kato, Masahide1 ; Okada, Noboru
1 Sophia University, Department of Mathematics, 7-1 Kioicho, Chiyoda-ku, Tokyo, 102-8554 (Japan)
Annales de l'Institut Fourier, Tome 54 (2004) no. 6, pp. 1827-1854.

On étudie le prolongement des applications holomorphes σ:H→X définies sur un ouvert de Hartogs H et à valeurs dans une variété holomorphe X. Pour les variétés kähleriennes compactes ainsi que pour certaines variétés compactes non kähleriennes le domaine maximal Ω σ de prolongement de σ au dessus du polydisque Δ est un domaine contenu dans Δ. Pour de telles variétés compactes, on définit, dans cet article, un invariant Hex n (X) qui utilise la dimension de Hausdorff de l’ensemble singulier de σ et on étudie ses propriétés afin d’en déduire des informations sur la structure complexe de X.

We study the extension problem of holomorphic maps σ:H→X of a Hartogs domain H with values in a complex manifold X. For compact Kähler manifolds as well as various non-Kähler manifolds, the maximal domain Ω σ of extension for σ over Δ is contained in a subdomain of Δ. For such manifolds, we define, in this paper, an invariant Hex n (X) using the Hausdorff dimensions of the singular sets of σ’s and study its properties to deduce informations on the complex structure of X.

DOI : 10.5802/aif.2068
Classification : 32D10, 32D15, 32H02, 32J17, 32J18
Keywords: extension of holomorphic map, envelope of holomorphy, non-Kähler manifold
Mot clés : prolongement des applications holomorphes, enveloppe d'holomorphie, variété non-kählérienne

Kato, Masahide 1 ; Okada, Noboru 

1 Sophia University, Department of Mathematics, 7-1 Kioicho, Chiyoda-ku, Tokyo, 102-8554 (Japan) 
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Kato, Masahide; Okada, Noboru. On holomorphic maps into compact non-Kähler manifolds. Annales de l'Institut Fourier, Tome 54 (2004) no. 6, pp. 1827-1854. doi : 10.5802/aif.2068. https://aif.centre-mersenne.org/articles/10.5802/aif.2068/

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