Compact quotients of large domains in complex projective space
Annales de l'Institut Fourier, Volume 48 (1998) no. 1, p. 223-246

We study compact complex manifolds covered by a domain in n-dimensional projective space whose complement E is non-empty with (2n-2)-dimensional Hausdorff measure zero. Such manifolds only exist for n3. They do not belong to the class 𝒞, so they are neither Kähler nor Moishezon, their Kodaira dimension is -, their fundamental groups are generalized Kleinian groups, and they are rationally chain connected. We also consider the two main classes of known 3-dimensional examples: Blanchard manifolds, for which E is a line, and the generalized Schottky coverings constructed by Nori. We determine their function fields and describe the surfaces they contain.

Nous étudions les variétés complexes compactes qui possèdent un revêtement qui soit un domaine dans l’espace projectif de dimension n dont le complémentaire E est un ensemble non vide de mesure de Hausdorff de dimension (2n-2) égale à zéro. De telles variétés n’existent que si n3. Elles n’appartiennent pas à la classe 𝒞, et par conséquent elles ne sont ni Kähler ni Moishezon, leur dimension de Kodaira est -, leurs groupes fondamentaux sont des groupes de Klein généralisés et elles sont connexes par chaînes rationnelles. Nous considérons aussi les deux classes principales d’exemples connus en dimension 3 : les variétés de Blanchard, pour lesquels E est une droite, et les revêtements généralisés de Schottky construits par Nori. Nous déterminons leur corps de fonctions méromorphes et décrivons les surfaces qu’elles contiennent.

@article{AIF_1998__48_1_223_0,
     author = {L\'arusson, Finnur},
     title = {Compact quotients of large domains in complex projective space},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {48},
     number = {1},
     year = {1998},
     pages = {223-246},
     doi = {10.5802/aif.1616},
     zbl = {0912.32020},
     mrnumber = {99d:32035},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1998__48_1_223_0}
}
Lárusson, Finnur. Compact quotients of large domains in complex projective space. Annales de l'Institut Fourier, Volume 48 (1998) no. 1, pp. 223-246. doi : 10.5802/aif.1616. http://www.numdam.org/item/AIF_1998__48_1_223_0/

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