On deformations of Fano manifolds

DOI10.1007/s00208-021-02226-2OpenAlexW3176381037MaRDI QIDQ2163421

Huai-Dong Cao, Xiaofeng Sun, Yingying Zhang, Shing Tung Yau

Publication date: 10 August 2022

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

Full work available at URL: https://arxiv.org/abs/2006.01355

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) Fano varieties (14J45) Kähler-Einstein manifolds (32Q20) Families, fibrations in algebraic geometry (14Dxx)

Related Items

A Weil-Petersson type metric on the space of Fano Kähler-Ricci solitons, Kähler-Ricci flow for deformed complex structures

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• K-polystability of Q-Fano varieties admitting Kähler-Einstein metrics
• Deformation of canonical metrics. I
• Hermitian curvature and plurisubharmonicity of energy on Teichmüller space
• The moduli space of extremal compact Kähler manifolds and generalized Weil-Petersson metrics
• On the locally complete families of complex analytic structures
• On a set of polarized Kähler metrics on algebraic manifolds
• The Kähler-Ricci flow with positive bisectional curvature
• The Kähler-Ricci flow and the \(\overline \partial\) operator on vector fields
• Einstein metrics and complex structures
• The Weil-Petersson geometry of the moduli space of SU(n\(\geq 3)\) (Calabi- Yau) manifolds. I
• Extremal Kähler metrics and complex deformation theory
• Kähler-Einstein metrics with positive scalar curvature
• An obstruction to the existence of Einstein Kaehler metrics
• Deformation of extremal metrics, complex manifolds and the relative Futaki invariant
• Extremal Kähler metrics on projectivized vector bundles
• Deligne pairings and the Knudsen-Mumford expansion
• On stability and the convergence of the Kähler-Ricci flow
• Sur les Espaces Homogènes Kählériens d’un Groupe de Lie Réductif
• The Kähler-Ricci flow and K-polystability
• The projectivity of the moduli space of stable curves. I: Preliminaries on "det" and "Div".
• On the ricci curvature of a compact kähler manifold and the complex monge-ampére equation, I
• On the lower order terms of the asymptotic expansion of Tian-Yau-Zelditch
• Kähler-Einstein metrics on Fano manifolds. I: Approximation of metrics with cone singularities
• Kähler-Einstein metrics on Fano manifolds. II: Limits with cone angle less than \boldmath2𝜋
• Kähler-Einstein metrics on Fano manifolds. III: Limits as cone angle approaches \boldmath2𝜋 and completion of the main proof
• Weil-Petersson metrics on deformation spaces