Quasi-isometry and deformations of Calabi-Yau manifolds

DOI10.1007/s00222-014-0516-1zbMath1318.32017arXiv1207.1182OpenAlexW1983811153MaRDI QIDQ2257726

Sheng Rao, Ke Feng Liu, Xiao Kui Yang

Publication date: 2 March 2015

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1207.1182

zbMATH Keywords

compact Kähler manifoldsHodge theoryKodaira-Spencer-Kuranishi deformation theory

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) Calabi-Yau manifolds (algebro-geometric aspects) (14J32) Calabi-Yau theory (complex-analytic aspects) (32Q25) Hodge theory in global analysis (58A14) Compact Kähler manifolds: generalizations, classification (32J27) Deformations of complex structures (32G05)

Related Items (20)

Extension formulae on almost complex manifolds ⋮ Holomorphic deformations of the Ricci-flat \(\partial \overline{\partial}\)-manifolds ⋮ Moishezon deformations of manifolds in Fujiki class \(\mathcal{C} \) ⋮ POWER SERIES PROOFS FOR LOCAL STABILITIES OF KÄHLER AND BALANCED STRUCTURES WITH MILD -LEMMA ⋮ Canonical sections of Hodge bundles on moduli spaces ⋮ Deformations of some open submanifolds of Calabi-Yau manifolds ⋮ Two applications of the \(\partial \overline{\partial}\)-Hodge theory ⋮ Geometry of the Maurer-Cartan equation near degenerate Calabi-Yau varieties ⋮ Deformations of compact complex manifolds with ample canonical bundles ⋮ Several special complex structures and their deformation properties ⋮ On Tian-Todorov lemma and its applications to deformation of CR-structures ⋮ Deformations of Dolbeault cohomology classes for Lie algebra with complex structures ⋮ Derivations on almost complex manifolds ⋮ The correspondence formula of Dolbeault complex on pair deformation ⋮ On the deformed Bott-Chern cohomology ⋮ Extension formulas and deformation invariance of Hodge numbers ⋮ Deformations of complex orbifolds and the period maps ⋮ Geometry of logarithmic forms and deformations of complex structures ⋮ On local stabilities of -Kähler structures ⋮ Deformations of Dolbeault cohomology classes

Cites Work

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• Remarks on the Cartan formula and its applications
• On the geometry of moduli spaces
• The Weil-Petersson geometry of the moduli space of SU(n\(\geq 3)\) (Calabi- Yau) manifolds. I
• Geometry of formal Kuranishi theory
• Periods of Integrals on Algebraic Manifolds, II: (Local Study of the Period Mapping)

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