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.
Dolbeault cohomology of complex nilmanifolds foliated in toroidal groups
A. Fino;
2019-01-01
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.
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