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

Abstract

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 three.

40 pages, revised version of the second part of arXiv:0709.0467v1. To appear in Proc. LMS

References in corpus (3)

• Lie-algebra Dolbeault cohomology and small deformations of nilmanifolds
• The Kuranishi-space of complex parallelisable nilmanifolds
• Hermitian structures on six dimensional nilmanifolds

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