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RELATIONS BETWEEN THE COHOMOLOGY GROUPS OF DOLBEAULT AND TOPOLOGICAL INVARIANTS [PDF]
Proceedings of the National Academy of Sciences of the United States of America, 1955 Frölicher A.
exaly +5 more sources
Dolbeault cohomology of compact complex manifolds with an action of a complex Lie group [PDF]
Journal of Geometry and Physics, 2020 Let $G$ be a complex Lie group acting on a compact complex Hermitian manifold $M$ by holomorphic isometries. We prove that the induced action on the Dolbeault cohomology and on the Bott-Chern cohomology is trivial. We also apply this result to compute the Dolbeault cohomology of Vaisman manifolds.
Nikita Klemyatin
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On the Hausdorff property of some Dolbeault cohomology groups [PDF]
Mathematische Zeitschrift, 2012 In this paper we formulate the duality for the Cauchy-Riemann complex in various function spaces and use the duality to study the Hausdorff property of Dolbeault cohomology groups.
Christine Laurent-Thiebaut +1 more
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Dolbeault cohomology of complex nilmanifolds foliated in toroidal groups [PDF]
The Quarterly Journal of Mathematics, 2019 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.
A. Fino, S. Rollenske, J. Ruppenthal
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Dolbeault Type Cohomology Groups of Infinitesimal Deformations and Their Applications
, 2023 In this paper, we establish a kind of Dolbeault type cohomology groups for the purpose of studying the varying of complex structure invariants in infinitesimal deformations of any order. We give a concrete description of the higher order Kodaria-Spencer maps by using these cohomology groups.
Lin, Jiezhu, Ye, Xuanming
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On Cohomology Groups of Certain Subcomplexes of Dolbeault Complexes [PDF]
Proceedings of the American Mathematical Society, 1973 The paper first shows that for a path connected topological group acting analytically on a complex manifold M M , the induced action on the cohomology groups of antiholomorphic forms on M M is trivial. By the same method it then shows that the cohomology groups of complex { ker
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On the infinite dimensionality of the Dolbeault cohomology groups [PDF]
Proceedings of the American Mathematical Society, 1975 Let M M be an open subset of a Stein manifold without isolated points. Let Ω p {\Omega ^p} be the sheaf of germs of holomorphic p p -forms on M M . Then H q ( M ,
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On Bott-Chern cohomology of compact complex surfaces [PDF]
, 2014 We study Bott-Chern cohomology on compact complex non-K\"ahler surfaces. In particular, we compute such a cohomology for compact complex surfaces in class $\text{VII}$ and for compact complex surfaces diffeomorphic to ...
Angella, Daniele +2 more
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Cohomological aspects on complex and symplectic manifolds [PDF]
, 2016 We discuss how quantitative cohomological informations could provide qualitative properties on complex and symplectic manifolds. In particular we focus on the Bott-Chern and the Aeppli cohomology groups in both cases, since they represent useful tools in
A. Aeppli +22 more
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Degree of non-K\"ahlerianity for 6-dimensional nilmanifolds [PDF]
, 2015 We use Bott-Chern cohomology to measure the non-K\"ahlerianity of 6-dimensional nilmanifolds endowed with the invariant complex structures in M. Ceballos, A. Otal, L. Ugarte, and R.
Angella, Daniele +2 more
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