Lie-algebra Dolbeault cohomology and small deformations of nilmanifolds
arXiv:0709.0467 · doi:10.1112/jlms/jdn076
Abstract
We consider nilmanifolds with left-invariant complex structure and prove that small deformations of such structures are again left invariant if the Dolbeault-cohomology of the nilmanifold can be calculated using left-invariant forms. By a result of Console and Fino this is generically the case. Our main tool is an analog of Dolbeault-cohomology for Lie-algebras with complex structure.
arXiv comment19 pages; updated first part of arXiv:0709.0467v1 containing the results on small deformations. The results on deformations in the large will appear in an independent paper
References in corpus (5)
Cited by in corpus (17)
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