Dolbeault cohomology of complex nilmanifolds foliated in toroidal groups
Differential Geometry
2018-08-27 v1 Complex Variables
Abstract
It is conjectured that the Dolbeault cohomology of a complex nilmanifold is computed by left-invariant forms. We prove this under the assumption that is suitably foliated in toroidal groups and deduce that the conjecture holds in real dimension up to six. Our approach generalises previous methods, where the existence of a holomorphic fibration was a crucial ingredient.
Keywords
Cite
@article{arxiv.1808.08090,
title = {Dolbeault cohomology of complex nilmanifolds foliated in toroidal groups},
author = {Anna Fino and Sönke Rollenske and Jean Ruppenthal},
journal= {arXiv preprint arXiv:1808.08090},
year = {2018}
}