Dolbeault cohomology of compact nilmanifolds
نویسندگان
چکیده
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 .
متن کاملDolbeault Cohomology and Deformations of Nilmanifolds
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...
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which is a symplectic analog of the well-known de Rham–Hodge ∗operator on oriented Riemannian manifolds: one should use the symplectic form instead of the Riemannian metric. Going further, one can define operator δ = ± ∗ d∗, δ = 0. The form α is called symplectically harmonic if dα = 0 = δα. However, unlike de Rham–Hodge case, there exist simplectically harmonic forms which are exact. Because o...
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Loop spaces LM of compact complex manifolds M promise to have rich analytic cohomology theories, and it is expected that sheaf and Dolbeault cohomology groups of LM will shed new light on the complex geometry and analysis of M itself. This idea first occurs in [W], in the context of the infinite dimensional Dirac operator, and then in [HBJ] that touches upon Dolbeault groups of loop spaces; but...
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In this survey article, we discuss some recent progress on tropical Dolbeault cohomology of varieties over non-Archimedean fields, a new cohomology theory based on real forms defined by Chambert-Loir and Ducros.
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ژورنال
عنوان ژورنال: Transformation Groups
سال: 2001
ISSN: 1083-4362,1531-586X
DOI: 10.1007/bf01597131