STABILITY OF ABELIAN COMPLEX STRUCTURES

DOI10.1142/S0129167X06003576zbMath1096.32009arXivmath/0506314OpenAlexW1972396672MaRDI QIDQ5470147

Yat Sun Poon, Sergio Console, Anna Fino

Publication date: 29 May 2006

Published in: International Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0506314

zbMATH Keywords

nilmanifoldDolbeault cohomologyAbelian complex structureKuranishi deformation family

Mathematics Subject Classification ID

Nilpotent and solvable Lie groups (22E25) Homogeneous complex manifolds (32M10) Deformations of complex structures (32G05)

Related Items (24)

On de Rham and Dolbeault cohomology of solvmanifolds ⋮ Abelian balanced Hermitian structures on unimodular Lie algebras ⋮ POWER SERIES PROOFS FOR LOCAL STABILITIES OF KÄHLER AND BALANCED STRUCTURES WITH MILD -LEMMA ⋮ Locally conformally Kähler solvmanifolds: a survey ⋮ Holomorphic Poisson structure and its cohomology on nilmanifolds ⋮ Almost Kähler structures on four dimensional unimodular Lie algebras ⋮ The Kuranishi space of complex parallelisable nilmanifolds ⋮ Maximal nilpotent complex structures ⋮ Several special complex structures and their deformation properties ⋮ Holomorphic Poisson cohomology ⋮ Generalized deformation of complex structures on nilmanifolds ⋮ Deformations of Dolbeault cohomology classes for Lie algebra with complex structures ⋮ A note on canonical Ricci forms on $2$-step nilmanifolds ⋮ Deformations of strong Kähler with torsion metrics ⋮ Generalized deformations and holomorphic Poisson cohomology of solvmanifolds ⋮ Chern-flat and Ricci-flat invariant almost Hermitian structures ⋮ Abelian Hermitian geometry ⋮ Complex, symplectic, and contact structures on low-dimensional Lie groups ⋮ Abelian complex structures and generalizations ⋮ Dolbeault cohomology of nilmanifolds with left-invariant complex structure ⋮ On local stabilities of -Kähler structures ⋮ Complex structures on nilpotent Lie algebras with one-dimensional center ⋮ On the Bott–Chern cohomology and balanced Hermitian nilmanifolds ⋮ Invariant complex structures on 6-nilmanifolds: classification, Frölicher spectral sequence and special Hermitian metrics

Cites Work

• On the locally complete families of complex analytic structures
• On the cohomology of compact homogeneous spaces of nilpotent Lie groups
• Compact nilmanifolds with nilpotent complex structures: Dolbeault cohomology
• Complex structures on nilpotent Lie algebras
• Dolbeault cohomology of compact nilmanifolds

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