Meromorphic Groups
复变函数
2007-05-23 v2 逻辑
摘要
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.
引用
@article{arxiv.math/0005023,
title = {Meromorphic Groups},
author = {Anand Pillay and Thomas Scanlon},
journal= {arXiv preprint arXiv:math/0005023},
year = {2007}
}
备注
The claim in Case III of the proof of Lemma 4.3 was missing in the earlier version