Lie-algebra Dolbeault cohomology and small deformations of nilmanifolds
Algebraic Geometry
2009-10-31 v2 Differential Geometry
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.
Keywords
Cite
@article{arxiv.0709.0467,
title = {Lie-algebra Dolbeault cohomology and small deformations of nilmanifolds},
author = {Sönke Rollenske},
journal= {arXiv preprint arXiv:0709.0467},
year = {2009}
}
Comments
19 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