An Integral Operator into Dolbeault Cohomology
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 کاملMonodromy Map for Tropical Dolbeault Cohomology
We define monodromy maps for tropical Dolbeault cohomology of algebraic varieties over non-Archimedean fields. We propose a conjecture of Hodge isomorphisms via monodromy maps, and provide some evidence.
متن کاملDolbeault Cohomology of a Loop Space
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...
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...
متن کاملTropical Dolbeault Cohomology of Non-archimedean Spaces
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: Journal of Functional Analysis
سال: 1996
ISSN: 0022-1236
DOI: 10.1006/jfan.1996.0050