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

Hwang, Jun-Muk, and Varolin, Dror. "A compactification of $({\mathbb {C}}^*)^4$ with no non-constant meromorphic functions." Annales de l’institut Fourier 52.1 (2002): 245-253. <http://eudml.org/doc/115975>.

@article{Hwang2002,
abstract = {For each 2-dimensional complex torus $T$, we construct a compact complex manifold $X(T)$ with a $\{\mathbb \{C\}\}^2$-action, which compactifies $(\{\mathbb \{C\}\}^*)^4$ such that the quotient of $(\{\mathbb \{C\}\}^*)^4$ by the $\{\mathbb \{C\}\}^2$-action is biholomorphic to $T$. For a general $T$, we show that $X(T)$ has no non-constant meromorphic functions.},
affiliation = {Korea Institute for Advanced Study, 207-43 Cheongryangri-dong, Séoul 130-012 (Corée Sud); University of Michigan, Department of Mathematics, Ann Arbor MI 48109-1109 (USA)},
author = {Hwang, Jun-Muk, Varolin, Dror},
journal = {Annales de l’institut Fourier},
keywords = {compactification; complex torus},
language = {eng},
number = {1},
pages = {245-253},
publisher = {Association des Annales de l'Institut Fourier},
title = {A compactification of $(\{\mathbb \{C\}\}^*)^4$ with no non-constant meromorphic functions},
url = {http://eudml.org/doc/115975},
volume = {52},
year = {2002},
}

TY - JOUR
AU - Hwang, Jun-Muk
AU - Varolin, Dror
TI - A compactification of $({\mathbb {C}}^*)^4$ with no non-constant meromorphic functions
JO - Annales de l’institut Fourier
PY - 2002
PB - Association des Annales de l'Institut Fourier
VL - 52
IS - 1
SP - 245
EP - 253
AB - For each 2-dimensional complex torus $T$, we construct a compact complex manifold $X(T)$ with a ${\mathbb {C}}^2$-action, which compactifies $({\mathbb {C}}^*)^4$ such that the quotient of $({\mathbb {C}}^*)^4$ by the ${\mathbb {C}}^2$-action is biholomorphic to $T$. For a general $T$, we show that $X(T)$ has no non-constant meromorphic functions.
LA - eng
KW - compactification; complex torus
UR - http://eudml.org/doc/115975
ER -