We study the extension problem of holomorphic maps of a Hartogs domain with values in a complex manifold . For compact Kähler manifolds as well as various non-Kähler manifolds, the maximal domain of extension for over is contained in a subdomain of . For such manifolds, we define, in this paper, an invariant Hex using the Hausdorff dimensions of the singular sets of ’s and study its properties to deduce informations on the complex structure of .
On étudie le prolongement des applications holomorphes définies sur un ouvert de Hartogs et à valeurs dans une variété holomorphe . Pour les variétés kähleriennes compactes ainsi que pour certaines variétés compactes non kähleriennes le domaine maximal de prolongement de au dessus du polydisque est un domaine contenu dans . Pour de telles variétés compactes, on définit, dans cet article, un invariant Hex qui utilise la dimension de Hausdorff de l’ensemble singulier de et on étudie ses propriétés afin d’en déduire des informations sur la structure complexe de .
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}, pages = {1827--1854}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {54}, number = {6}, year = {2004}, doi = {10.5802/aif.2068}, mrnumber = {2134226}, zbl = {1077.32003}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2068/} }
TY - JOUR TI - On holomorphic maps into compact non-Kähler manifolds JO - Annales de l'Institut Fourier PY - 2004 DA - 2004/// SP - 1827 EP - 1854 VL - 54 IS - 6 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2068/ UR - https://www.ams.org/mathscinet-getitem?mr=2134226 UR - https://zbmath.org/?q=an%3A1077.32003 UR - https://doi.org/10.5802/aif.2068 DO - 10.5802/aif.2068 LA - en ID - AIF_2004__54_6_1827_0 ER -
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. https://aif.centre-mersenne.org/articles/10.5802/aif.2068/
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