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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Meromorphic groups


Authors: Anand Pillay and Thomas Scanlon
Journal: Trans. Amer. Math. Soc. 355 (2003), 3843-3859
MSC (2000): Primary 30Dxx
Published electronically: June 24, 2003
MathSciNet review: 1990567
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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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Additional Information

Anand Pillay
Affiliation: Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801
Email: pillay@math.uiuc.edu

Thomas Scanlon
Affiliation: Department of Mathematics, University of California at Berkeley, Berkeley, California 94720-3840
Email: scanlon@math.berkeley.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-03-03383-X
PII: S 0002-9947(03)03383-X
Received by editor(s): June 16, 2000
Published electronically: June 24, 2003
Additional Notes: The first author was partially supported by an NSF grant; the second, by an NSF MSPRF
Article copyright: © Copyright 2003 American Mathematical Society