Dolbeault Cohomology and Deformations of Nilmanifolds
نویسندگان
چکیده
In these notes I review some classes of invariant complex structures on nilmanifolds for which the Dolbeault cohomology can be computed by means of invariant forms, in the spirit of Nomizu’s theorem for de Rham cohomology. Moreover, deformations of complex structures are discussed. Small deformations remain in some cases invariant, so that, by Kodaira-Spencer theory, Dolbeault cohomology can be still computed using invariant forms.
منابع مشابه
Dolbeault Cohomology of compact Nilmanifolds
Let M = G/Γ be a compact nilmanifold endowed with an invariant complex structure. Using a descending series associated to the complex structure and the Borel spectral sequences for the corresponding set of holomorphic fibrations, we prove a version of Nomizu’s Theorem for the Dolbeault cohomology of M .
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