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.
2019
70
1265
1279
https://academic.oup.com/qjmath/article/70/4/1265/5527137?guestAccessKey=e3bd60ee-1908-43bd-bac4-52d03c7e3544
A. Fino, S. Rollenske, J. Ruppenthal
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/1719726
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