Dolbeault cohomology of complex nilmanifolds foliated in toroidal groups
Copyright policy )Dolbeault cohomology of complex nilmanifolds foliated in toroidal groups
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.
- University of Turin Italy
- University of Wuppertal Germany
- Philipps-University of Marburg Germany
Mathematics - Differential Geometry, Differential Geometry (math.DG), Mathematics - Complex Variables, 22E25 (primary) 37F75, 53C30, 53C15 (secondary), FOS: Mathematics, Complex Variables (math.CV)
Mathematics - Differential Geometry, Differential Geometry (math.DG), Mathematics - Complex Variables, 22E25 (primary) 37F75, 53C30, 53C15 (secondary), FOS: Mathematics, Complex Variables (math.CV)
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