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
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
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.