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32-XX Several complex variables and analytic spaces
32Jxx Compact analytic spaces
32J05 Compactification of analytic spaces

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

Jun-Muk Hwang, Dror Varolin (2002)

Annales de l’institut Fourier

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.