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Meromorphic groups
Author(s):
Anand
Pillay;
Thomas
Scanlon
Journal:
Trans. Amer. Math. Soc.
355
(2003),
3843-3859.
MSC (2000):
Primary 30Dxx
Posted:
June 24, 2003
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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:
10.1090/S0002-9947-03-03383-X
PII:
S 0002-9947(03)03383-X
Received by editor(s):
June 16, 2000
Posted:
June 24, 2003
Additional Notes:
The first author was partially supported by an NSF grant; the second, by an NSF MSPRF
Copyright of article:
Copyright
2003,
American Mathematical Society
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