Geometry of twisted Kähler-Einstein metrics and collapsing

DOI10.1007/s00220-020-03911-0zbMath1469.32018arXiv1911.07315OpenAlexW3096620754MaRDI QIDQ2216776

Mark Gross, Yuguang Zhang, Valentino Tosatti

Publication date: 17 December 2020

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1911.07315

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) Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Kähler-Einstein manifolds (32Q20)

Related Items

Second-order estimates for collapsed limits of Ricci-flat Kähler metrics, Calabi symmetry and the continuity method, On the collapsing of Calabi-Yau manifolds and Kähler-Ricci flows, Curvature estimates for the continuity method, Higher-order estimates of long-time solutions to the Kähler-Ricci flow

Cites Work

• 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
• Conic singularities metrics with prescribed Ricci curvature: general cone angles along normal crossing divisors
• Continuity of extremal transitions and flops for Calabi-Yau manifolds
• Triviality of fibered Calabi-Yau manifolds without singular fibers
• Gromov-Hausdorff collapsing of Calabi-Yau manifolds
• Igusa integrals and volume asymptotics in analytic and adelic geometry
• Convergence of Calabi-Yau manifolds
• Sectional curvatures of Kähler moduli
• Toroidal embeddings. I
• Plurisubharmonische Funktionen in komplexen Räumen
• Higher-order estimates for collapsing Calabi-Yau metrics
• Limits of Calabi-Yau metrics when the Kähler class degenerates
• Infinite-time singularities of the Kähler-Ricci flow
• Adiabatic limits of Ricci-flat Kähler metrics
• Extension of twisted Hodge metrics for Kähler morphisms
• The asymptotic behavior of a variation of polarized Hodge structure
• On fiber products of rational elliptic surfaces with section
• Existence and degeneration of Kähler-Einstein metrics on minimal algebraic varieties of general ype
• Limits of Hodge structures
• On Kähler fiber spaces over curves
• Deformations of calibrated submanifolds
• Special Kähler manifolds
• On the incompleteness of the Weil-Petersson metric along degenerations of Calabi-Yau manifolds
• The complex Monge-Ampère equation
• Variation of Hodge structure: The singularities of the period mapping
• Quasi-Hodge metrics and canonical singularities.
• The moduli space of complex Lagrangian submanifolds
• Large complex structure limits of \(K3\) surfaces
• Functorial desingularization over \(\mathbb Q\): boundaries and the embedded case
• Collapsing \(K3\) surfaces and moduli compactification
• Convergence of weak Kähler-Ricci flows on minimal models of positive Kodaira dimension
• Degeneration of Hodge structures
• Développement asymptotique des fonctions obtenues par intégration sur les fibres
• Collapsing of abelian fibered Calabi-Yau manifolds
• Some progresses on Kähler-Ricci flow
• Tropical and non-Archimedean limits of degenerating families of volume forms
• On collapsing Calabi-Yau fibrations
• Adiabatic limits of anti-self-dual connections on collapsed \(K3\) surfaces
• Geometric estimates for complex Monge-Ampère equations
• Twisted constant scalar curvature Kähler metrics and Kähler slope stability
• A gluing construction of collapsing Calabi-Yau metrics on \(K3\) fibred 3-folds
• Collapsing limits of the Kähler-Ricci flow and the continuity method
• Fibrations with constant scalar curvature Kähler metrics and the CM-line bundle
• The Kähler-Ricci flow on surfaces of positive Kodaira dimension
• The collapsing rate of the Kähler-Ricci flow with regular infinite time singularity
• Locally homogeneous complex manifolds
• Asymptotic expansions of fiber integrals over higher-dimensional bases
• Smooth and Singular Kähler–Einstein Metrics
• Canonical measures and Kähler-Ricci flow
• Gravitational instantons from rational elliptic surfaces
• Singular Kähler-Einstein metrics
• Bounding scalar curvature for global solutions of the Kähler-Ricci flow
• On the singularities of the pluricomplex Green's function
• Collapsing hyperkähler manifolds
• Topics in Transcendental Algebraic Geometry. (AM-106)
• Families of Calabi–Yau Manifolds and Canonical Singularities
• A remark on Kähler metrics with conical singularities along a simple normal crossing divisor
• Remarks on the collapsing of torus fibered Calabi–Yau manifolds
• Hodge metrics and the curvature of higher direct images
• A General Schwarz Lemma for Kahler Manifolds
• On the ricci curvature of a compact kähler manifold and the complex monge-ampére equation, I
• Monge-Ampere equation on compact Kahler manifolds
• The moduli space of special Lagrangian submanifolds
• The Kähler-Ricci flow, Ricci-flat metrics and collapsing limits
• KAWA lecture notes on the K\"ahler-Ricci flow
• Singularities of metrics on Hodge bundles and their topological invariants
• A filling-in problem and moderate degenerations of minimal algebraic varieties
• Estimations $\mathrm{L}^2$ pour l'opérateur $\bar \partial$ d'un fibré vectoriel holomorphe semi-positif au-dessus d'une variété kählérienne complète
• On the Picard-Lefschetz Transformation for Algebraic Manifolds Acquiring General Singularities
• Extension of plurisubharmonic functions with growth control
• Metrics with cone singularities along normal crossing divisors and holomorphic tensor fields
• Hodge metrics and positivity of direct images
• Ricci Flat Kähler Metrics with Edge Singularities
• Products of harmonic forms and rational curves
• Kähler-Einstein metrics with edge singularities