Meromorphic Groups
Meromorphic Groups
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亚形群
DOI：
10.1090/s0002-9947-03-03383-x
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发表时间：
2000
影响因子：
0.9
通讯作者：
T. Scanlon
中科院分区：
文献类型：
--
作者：
A. Pillay;T. Scanlon
我们引进的概念，一个亚纯群，削弱有点藤木的定义，我们证明了亚纯群是亚纯的扩展复环面的线性代数群，推广结果[藤木，1978年]。该结果的一个特例，也是证明中的一个要素，是强极小“模”亚纯群是复环面，回答了Hrushovski的一个问题。因此，我们表明，一个简单的紧凑复杂的流形有代数和库默维数为零，当且仅当其通用类型是平凡的。
We introduce the notion of a meromorphic group, weakening somewhat Fujiki's definition We prove that a meromorphic group is meromorphically an extension of a complex torus by a linear algebraic group, generalizing results in [Fujiki, 1978]. A special case of this result, as well as one of the ingredients in the proof, is that a strongly minimal"modular"meromorphic group is a complex torus, answering a question of Hrushovski. As a consequence, we show that a simple compact complex manifold has algebraic and Kummer dimension zero if an only if its generic type is trivial.