English

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 XX is computed by left-invariant forms. We prove this under the assumption that XX 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}
}