no. 1
A compactification of (ℂ * ) 4 with no non-constant meromorphic functions
[Une compactification de (ℂ * ) 4 sans fonction méromorphe non constante]
Hwang, Jun-Muk1 ; Varolin, Dror2
1 Korea Institute for Advanced Study, 207-43 Cheongryangri-dong, Séoul 130-012 (Corée Sud)
2 University of Michigan, Department of Mathematics, Ann Arbor MI 48109-1109 (USA)
Annales de l'Institut Fourier, Tome 52 (2002) no. 1, pp. 245-253

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.

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.

DOI : 10.5802/aif.1884
Classification : 32J05, 32M05
Keywords: compactification, complex torus
Mots-clés : compactification, tore complexe

Hwang, Jun-Muk 1 ; Varolin, Dror 2

1 Korea Institute for Advanced Study, 207-43 Cheongryangri-dong, Séoul 130-012 (Corée Sud)
2 University of Michigan, Department of Mathematics, Ann Arbor MI 48109-1109 (USA) 
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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

[DPS] J.-P. Demailly; T. Peternell; M. Schneider Compact complex manifolds with numerically effective tangent bundles, J. Alg. Geom., Volume 3 (1994), pp. 295-345 | Zbl | MR

[G] C. Gellhaus Äquivariante Kompaktifizierungen des ℂ n , Math. Zeit., Volume 206 (1991), pp. 211-217 | Zbl | MR

[H] R. Hartshorne Ample subvarieties of algebraic varieties, Lecture Notes in Mathematics, Vol. 156, Springer-Verlag, Berlin-Heidelberg-New York, 1970 | Zbl | MR

[KP] S. Kosarew; T. Peternell Formal cohomology, analytic cohomology and non-algebraic manifolds, Compositio Math, Volume 74 (1990), pp. 299-325 | Zbl | MR | Numdam

[PS] T. Peternell; M. Schneider Compactifications of ℂ n : A survey, Proc. Symp. Pure Math, Volume 52 (1991) no. Part 2, pp. 455-466 | Zbl | MR

[RR] J.-P. Rosay; W. Rudin Holomorphic maps from ℂ n to ℂ n , Trans. Amer. Math. Soc., Volume 310 (1988), pp. 47-86 | Zbl | MR

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