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Holomorphic approximation via Dolbeault cohomology [PDF]
Mathematische Zeitschrift, 2020 The purpose of this paper is to study holomorphic approximation and approximation of $\bar\partial$-closed forms in complex manifolds of complex dimension $n\geq 1$. We consider extensions of the classical Runge theorem and the Mergelyan property to domains in complex manifolds for the smooth and the $L^2$ topology.
Mei-Chi Shaw +1 more
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Note on Dolbeault cohomology and Hodge structures up to bimeromorphisms [PDF]
Complex Manifolds, 2020 We construct a simply-connected compact complex non-Kähler manifold satisfying the ∂ ̅∂ -Lemma, and endowed with a balanced metric. To this aim, we were initially aimed at investigating the stability of the property of satisfying the ∂ ̅∂-Lemma under ...
Adriano Tomassini +2 more
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Dolbeault cohomology for almost complex manifolds [PDF]
Advances in Mathematics, 2021 Minor corrections and updates.
Joana Cirici, Scott Wilson
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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.
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.
exaly +5 more sources
Deformations of Dolbeault cohomology classes [PDF]
Mathematische Zeitschrift, 2021 46 pages, published version (https://doi.org/10.1007/s00209-021-02900-w)
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Dolbeault cohomology of compact nilmanifolds [PDF]
Transformation Groups, 2001 15 pages, Latex, to appear in Transformation ...
Anna Fino
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Leray–Hirsch theorem and blow-up formula for Dolbeault cohomology [PDF]
Annali Di Matematica Pura Ed Applicata, 2020 We prove a theorem of Leray-Hirsch type and give an explicit blow-up formula for Dolbeault cohomology on (\emph{not necessarily compact}) complex manifolds. We give applications to strongly $q$-complete manifolds and the $\partial\bar{\partial}$-lemma.
Lingxu Meng
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Twisted basic Dolbeault cohomology on transverse Kähler foliations
Annals of Global Analysis and Geometry, 2022 18 pages.
Seoung Dal Jung, Seoung Dal Jung
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Holomorphic Koszul–Brylinski homology via Dolbeault cohomology
Geometriae Dedicata, 2022 15 ...
Lingxu Meng
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