Meromorphic Groups

Details Meromorphic Groups Meromorphic Groups

2000-05-02

arxiv.org/abs/math/0005023v2

Mathematics

Complex Variables

The claim in Case III of the proof of Lemma 4.3 was missing in the earlier version

Scientific paper

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.

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