Meromorphic groups

Pillay, Anand; Scanlon, Thomas

doi:10.1090/S0002-9947-03-03383-X

Meromorphic groups
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by Anand Pillay and Thomas Scanlon PDF

Trans. Amer. Math. Soc. 355 (2003), 3843-3859 Request permission

Abstract:

We show that a connected group interpretable in a compact complex manifold (a meromorphic group) is definably an extension of a complex torus by a linear algebraic group, generalizing results of Fujiki. 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 and only if its generic type is trivial.

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