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On Arithmetic Genera of Algebraic Varieties. [PDF]

Proc Natl Acad Sci U S A, 1953
Kodaira K, Spencer DC.
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Dolbeault cohomology and deformations of nilmanifolds

, 2006
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.
Console, Sergio, Sergio Console
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Dolbeault Cohomology for G2-Manifolds

Geometriae Dedicata, 1998
Cocalibrated \(G_2\)-manifolds are 7-dimensional Riemannian manifolds with a distinguished 3-form which is coclosed. \textit{S. Salamon} [in `Riemannian geometry and holonomy groups' (Pitman Res. Notes Math. Ser. 201, Longman, Harlow) (1989; Zbl 0685.53001)] defined a differential complex \(({\mathcal A}^q (M), \breve D_q)\) related with the \(G_2 ...
Fernández, Marisa, Ugarte, Luis
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Dolbeault cohomology of G/(P,P)

Mathematische Zeitschrift, 1999
Let \(G\) be a complex connected semisimple Lie group with parabolic subgroup \(P\). Let \((P,P)\) be its commutator subgroup. The generalized Borel-Weil theorem on flag manifolds has an analogous result on the Dolbeault cohomology \(H^{0,q}(G/(P,P))\). Consequently, the dimension of \(H^{0,q}(G/(P,P))\) is either 0 or \(\infty\).
Chuah, Meng-Kiat, Teo, Lee-Peng
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Laplace hyperfunctions via Čech-Dolbeault cohomology

2022
The paper studies several properties of Laplace hyperfunctions introduced by H.~Komatsu in the one dimensional case and by the authors in the higher dimensional cases from the viewpoint of Čech-Dolbeault cohomology theory, which enables us, for example, to construct the Laplace transformation and its inverse in a simple way.
Honda, Naofumi, Umeta, Kohei
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On the Sobolev Dolbeault cohomology of a domain with pseudoconcave boundaries

Acta Mathematica Scientia, 2023
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Dolbeault cohomology of compact complex manifolds with an action of a complex Lie group

Journal of Geometry and Physics, 2020
Nikita Klemyatin
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Deformations of Dolbeault cohomology classes for Lie algebra with complex structures

Annals of Global Analysis and Geometry, 2021

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Representations in Dolbeault cohomology

2000
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Group actions on the Dolbeault cohomology of homogeneous manifolds

Mathematische Zeitschrift, 1997
Dmitri Akhiezer
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