A compactification of $({\mathbb {C}}^*)^4$ with no non-constant meromorphic functions

Hwang, Jun-Muk; Varolin, Dror

A compactification of

{(ℂ^{*})}^{4}

with no non-constant meromorphic functions
[Une compactification de

{(ℂ^{*})}^{4}

sans fonction méromorphe non constante]

Hwang, Jun-Muk ; Varolin, Dror

Annales de l'Institut Fourier, Tome 52 (2002), p. 245-253 / Harvested from Numdam

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Résumé
Abstract

Pour tout tore complexe $T$ de dimension 2, nous construisons une variété complexe compacte $X (T)$ munie d’une action de $ℂ^{2}$ qui compactifie ${(ℂ^{*})}^{4}$ de sorte que le quotient de ${(ℂ^{*})}^{4}$ par l’action de $ℂ^{2}$ 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 $ℂ^{2}$ -action, which compactifies ${(ℂ^{*})}^{4}$ such that the quotient of ${(ℂ^{*})}^{4}$ by the $ℂ^{2}$ -action is biholomorphic to $T$ . For a general $T$ , we show that $X (T)$ has no non-constant meromorphic functions.

Publié le : 2002-01-01

Zbl 0995.32011

DOI : https://doi.org/10.5802/aif.1884
Classification: 32J05, 32M05
Mots clés: compactification, tore complexe

@article{AIF_2002__52_1_245_0,
     author = {Hwang, Jun-Muk and Varolin, Dror},
     title = {A compactification of $({\mathbb {C}}^*)^4$ with no non-constant meromorphic functions},
     journal = {Annales de l'Institut Fourier},
     volume = {52},
     year = {2002},
     pages = {245-253},
     doi = {10.5802/aif.1884},
     zbl = {0995.32011},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_2002__52_1_245_0}
}

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) pp. 245-253. doi : 10.5802/aif.1884. http://gdmltest.u-ga.fr/item/AIF_2002__52_1_245_0/

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