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arXiv · 1808.08090

Dolbeault cohomology of complex nilmanifolds foliated in toroidal groups

Anna Fino·Sönke Rollenske·Jean Ruppenthal
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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 generalises previous methods, where the existence of a holomorphic fibration was a crucial ingredient.

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Anna Fino, Sönke Rollenske, Jean Ruppenthal. 2018-08-24. Dolbeault cohomology of complex nilmanifolds foliated in toroidal groups. https://arxiv.org/abs/1808.08090

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