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Proceedings of the London Mathematical Society Advance Access originally published online on March 4, 2009
Proceedings of the London Mathematical Society 2009 99(2):425-460; doi:10.1112/plms/pdp001
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© 2009 London Mathematical Society

Geometry of nilmanifolds with left-invariant complex structure and deformations in the large

Sönke Rollenske

Department of Mathematics
Imperial College London
SW7 2AZ London
United Kingdom

Received 4 September 2007. Revision received 22 April 2008.

The relation between nilmanifolds with left-invariant complex structure and iterated principal holomorphic torus bundles is clarified and we give criteria under which deformations in the large are again of such type. As an application we obtain a fairly complete picture in complex dimension 3.

2000 Mathematics Subject Classification 32G05 (32G08, 17B30, 53C30).


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