On holomorphic maps into compact non-Kähler manifolds
Annales de l'Institut Fourier, Volume 54 (2004) no. 6, p. 1827-1854
We study the extension problem of holomorphic maps σ:HX 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.
On étudie le prolongement des applications holomorphes σ:HX 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.
DOI : https://doi.org/10.5802/aif.2068
Classification:  32D10,  32D15,  32H02,  32J17,  32J18
Keywords: extension of holomorphic map, envelope of holomorphy, non-Kähler manifold
@article{AIF_2004__54_6_1827_0,
     author = {Kato, Masahide and Okada, Noboru},
     title = {On holomorphic maps into compact non-K\"ahler manifolds},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {54},
     number = {6},
     year = {2004},
     pages = {1827-1854},
     doi = {10.5802/aif.2068},
     zbl = {1077.32003},
     mrnumber = {2134226},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2004__54_6_1827_0}
}
Kato, Masahide; Okada, Noboru. On holomorphic maps into compact non-Kähler manifolds. Annales de l'Institut Fourier, Volume 54 (2004) no. 6, pp. 1827-1854. doi : 10.5802/aif.2068. http://www.numdam.org/item/AIF_2004__54_6_1827_0/

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