A compactification of ( * ) 4 with no non-constant meromorphic functions
[Une compactification de ( * ) 4 sans fonction méromorphe non constante]
Annales de l'Institut Fourier, Tome 52 (2002) no. 1, pp. 245-253.

Pour tout tore complexe T de dimension 2, nous construisons une variété complexe compacte X(T) munie d’une action de 2 qui compactifie ( * ) 4 de sorte que le quotient de ( * ) 4 par l’action de 2 soit biholomorphe à T. Pour un tore général T, nous montrons que X(T) n’a pas de fonction méromorphe non constante.

For each 2-dimensional complex torus T, we construct a compact complex manifold X(T) with a 2 -action, which compactifies ( * ) 4 such that the quotient of ( * ) 4 by the 2 -action is biholomorphic to T. For a general T, we show that X(T) has no non-constant meromorphic functions.

DOI : https://doi.org/10.5802/aif.1884
Classification : 32J05,  32M05
Mots clés : compactification, tore complexe
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     title = {A compactification of $({\mathbb {C}}^*)^4$ with no non-constant meromorphic functions},
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     pages = {245--253},
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Hwang, Jun-Muk; Varolin, Dror. A compactification of $({\mathbb {C}}^*)^4$ with no non-constant meromorphic functions. Annales de l'Institut Fourier, Tome 52 (2002) no. 1, pp. 245-253. doi : 10.5802/aif.1884. http://archive.numdam.org/articles/10.5802/aif.1884/

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