Dolbeault cohomology of complex nilmanifolds foliated in toroidal groups Article

Fino, A, Rollenske, S, Ruppenthal, J. (2019). Dolbeault cohomology of complex nilmanifolds foliated in toroidal groups . QUARTERLY JOURNAL OF MATHEMATICS, 70(4), 1265-1279. 10.1093/qmath/haz017

cited authors

  • Fino, A; Rollenske, S; Ruppenthal, J

authors

abstract

  • It is conjectured that the Dolbeault cohomology of a complex nilmanifold $X$ is computed by left-invariant forms. We prove this under the assumption that $X$ is suitably foliated in toroidal groups and deduce that the conjecture holds in real dimension up to six. Our approach generalizes previous methods, where the existence of a holomorphic fibration was a crucial ingredient.

publication date

  • December 1, 2019

published in

Digital Object Identifier (DOI)

start page

  • 1265

end page

  • 1279

volume

  • 70

issue

  • 4