Techniques of computations of Dolbeault cohomology of solvmanifolds

DOI10.1007/s00209-012-1013-0zbMath1261.22009arXiv1107.4761OpenAlexW2086487349MaRDI QIDQ1936619

Hisashi Kasuya

Publication date: 6 February 2013

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1107.4761

zbMATH Keywords

Dolbeault cohomologysolvmanifoldholomorphic line bundleinvariant complex structure

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Global differential geometry of Hermitian and Kählerian manifolds (53C55) Nilpotent and solvable Lie groups (22E25)

Related Items (17)

Locally conformal Hermitian metrics on complex non-Kähler manifolds ⋮ On de Rham and Dolbeault cohomology of solvmanifolds ⋮ POWER SERIES PROOFS FOR LOCAL STABILITIES OF KÄHLER AND BALANCED STRUCTURES WITH MILD -LEMMA ⋮ The cohomologies of the Iwasawa manifold and of its small deformations ⋮ On Dolbeault formality and small deformations ⋮ Deformations of balanced metrics ⋮ Hodge symmetry and decomposition on non-Kähler solvmanifolds ⋮ Bott-Chern cohomology of solvmanifolds ⋮ Holomorphic deformations of balanced Calabi-Yau $\partial \bar{\partial}$-manifolds ⋮ Frölicher spectral sequence and Hodge structures on the cohomology of complex parallelisable manifolds ⋮ Hodge theory for twisted differentials ⋮ Deformations of Dolbeault cohomology classes for Lie algebra with complex structures ⋮ Some results on the Hard Lefschetz Condition ⋮ Generalized deformations and holomorphic Poisson cohomology of solvmanifolds ⋮ The Frölicher spectral sequence of certain solvmanifolds ⋮ On local stabilities of -Kähler structures ⋮ On Bott-Chern cohomology and formality

Cites Work

• Small deformations and non-left-invariant complex structures on six-dimensional compact solvmanifolds
• On compact complex parallelisable solvmanifolds
• On the cohomology of compact homogeneous spaces of nilpotent Lie groups
• Lie-algebra Dolbeault-cohomology and small deformations of nilmanifolds
• Dolbeault Homotopy Theory
• Compact nilmanifolds with nilpotent complex structures: Dolbeault cohomology
• The deformation theory of representations of fundamental groups of compact Kähler manifolds
• Dolbeault cohomology of compact nilmanifolds
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