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Zbl 0994.32018
Bosio, Frédéric
Compact complex manifolds: an extension of Meersseman's and López de Medrano-Verjovsky's construction. (Variétés complexes compactes : une généralisation de la construction de Meersseman et López de Medrano-Verjovsky.) (French)
[J] Ann. Inst. Fourier 51, No.5, 1259-1297 (2001). ISSN 0373-0956; ISSN 1777-5310/e

The game is to construct nice classes of compact complex manifolds without any symplectic structure. In this paper the author wins at this game and gives strong generalizations of {\it S. López de Medrano} and {\it A. Verjovsky} [Bol. Soc. Bras. Mat., Nova Ser. 28, No. 2, 253-269 (1997; Zbl 0901.53021)] and of {\it L. Meersseman} [A new geometric construction of compact complex manifolds in any dimension, Math. Ann. 317, 79-115 (2000; Zbl 0958.32013)]. The manifolds are obtained as quotient of a large open subset of $\bbfC^n$ by a free action of the abelian group $\bbfC^m\times \bbfC^*$. The author gives a precise description of when one of these actions gives a compact smooth quotient.
[Edoardo Ballico (Povo)]

MSC 2000:: *32J18 Compact $n$-folds $(n \ge 4)$ (analytic spaces)
32M05 Automorphism groups of complex spaces
32Q99 Complex manifolds
05A05 Combinatorial choice problems

Keywords: compact complex manifolds; complex abelian Lie groups; combinatorics on finite sets; free action; cocompact subgroup; symplectic structure; compact complex manifold without symplectic structure; holomorphic quotient variety

Citations: Zbl 0901.53021; Zbl 0958.32013

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