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.
Mei-Chi Shaw +1 more
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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.
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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 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 ...
Shaw Mong
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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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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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Duality of Hodge numbers of compact complex nilmanifolds
Complex Manifolds, 2015 A compact K¨ahlerian manifoldM of dimension n satisfies hp,q(M) = hq,p(M) for each p, q.However, a compact complex manifold does not satisfy the equations in general. In this paper, we consider duality of Hodge numbers of compact complex nilmanifolds.
Yamada Takumi
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Hodge numbers and invariant complex structures of compact nilmanifolds
Complex Manifolds, 2016 In this paper, we consider several invariant complex structures on a compact real nilmanifold, and we study relations between invariant complex structures and Hodge numbers.
Yamada Takumi
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Remarks on Hodge numbers and invariant complex structures of compact nilmanifolds
Complex Manifolds, 2016 If N is a simply connected real nilpotent Lie group with a Γ-rational complex structure, where Γ is a lattice in N, then for each s, t.We study relations between invariant complex structures and Hodge numbers of compact nilmanifolds from a ...
Yamada Takumi
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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
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