Dolbeault Cohomology of compact Nilmanifolds

Details Dolbeault Cohomology of compact Nilmanifolds Dolbeault Cohomology of compact Nilmanifolds

1998-03-27

arxiv.org/abs/math/9803135v2

Mathematics

Differential Geometry

15 pages, Latex, to appear in Transformation Groups

Scientific paper

Let $M= G/\Gamma$ 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.

Affiliated with

Also associated with

No associations

Rating

Dolbeault Cohomology of compact Nilmanifolds does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Dolbeault Cohomology of compact Nilmanifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Dolbeault Cohomology of compact Nilmanifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-611735