Dolbeault Cohomology of compact Nilmanifolds
| dc.creator | Console, S. | |
| dc.creator | Fino, A. | |
| dc.date | 1998-03-27 | |
| dc.date | 2001-01-23 | |
| dc.date.accessioned | 2026-07-07T05:24:13Z | |
| dc.date.available | 2026-07-07T05:24:13Z | |
| dc.description | Let $M= G/Γ$ be a compact nilmanifold endowed with an invariant complex structure. We prove that, on an open set of any connected component of the moduli space ${\cal C} ({\frak g})$ of invariant complex structures on $M$, the Dolbeault cohomology of $M$ is isomorphic to the one of the differential bigraded algebra associated to the complexification $\cg^\C$ of the Lie algebra of $G$. To obtain this result, we first prove the above isomorphism for compact nilmanifolds endowed with a rational invariant complex structure. This is done using a descending series associated to the complex structure and the Borel spectral sequences for the corresponding set of holomorphic fibrations. Then we apply the theory of Kodaira-Spencer for deformations of complex structures. | |
| dc.description | 15 pages, Latex, to appear in Transformation Groups | |
| dc.identifier | https://arxiv.org/abs/math/9803135 | |
| dc.identifier | http://arxiv.org/abs/math/9803135 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76752 | |
| dc.subject | Differential Geometry | |
| dc.title | Dolbeault Cohomology of compact Nilmanifolds | |
| dc.type | text |