Nilmanifolds: complex structures, geometry and deformations

We consider nilmanifolds with left-invariant complex structure and prove that in the generic case small deformations of such structures are again left-invariant. The relation between nilmanifolds 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 dimension three. We show by example that the Frölicher spectral sequence of a nilmanifold may be arbitrarily non degenerate thereby answering a question mentioned in the book of Griffith and Harris. On our way we prove Serre Duality for Lie algebra Dolbeault cohomology and classify complex structures on nilpotent Lie algebras with small commutator subalgebra. MS Subject classification: 32G05; (32G08, 17B30, 53C30, 32C10)

Level thesis:degree_level

thesis.doctoral

Grantor dc:publisher

Universität Bayreuth

Year

2007

Author dc:creator

• Rollenske, Sönke

Contributors dc:contributor

• Catanese, Fabrizio

Repository record source_url

https://epub.uni-bayreuth.de/id/eprint/720/

OAI identifier oai:identifier

oai:epub.uni-bayreuth.de:720