Variation of singular Kähler-Einstein metrics: Kodaira dimension zero (with an appendix by Valentino Tosatti)

DOI10.4171/JEMS/1184MaRDI QIDQ2693152

Junyan Cao, Henri Guenancia, Mihai Paun

Publication date: 17 March 2023

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1908.08087

zbMATH Keywords

conic Kähler metricsKähler fiber spacedirect image of log pluricanonical bundleslog Calabi-Yau manifolds

Mathematics Subject Classification ID

Calabi-Yau manifolds (algebro-geometric aspects) (14J32) Families, moduli, classification: algebraic theory (14J10) Kähler-Einstein manifolds (32Q20)

Related Items (3)

Existence of the equivariant minimal model program for compact Kähler threefolds with the action of an abelian group of maximal rank ⋮ Families of singular Kähler-Einstein metrics ⋮ The space of finite-energy metrics over a degeneration of complex manifolds

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Conic singularities metrics with prescribed Ricci curvature: general cone angles along normal crossing divisors
• Singularities of Narasimhan-Simha type metrics on direct images of relative pluricanonical bundles
• Relative Kähler-Ricci flows and their quantization
• Numerical character of the effectivity of adjoint line bundles
• Kodaira dimension of algebraic fiber spaces over abelian varieties
• Monge-Ampère equations in big cohomology classes
• Convergence of Calabi-Yau manifolds
• Strict and nonstrict positivity of direct image bundles
• Torsion points on the cohomology jump loci of compact Kähler manifolds
• Bergman kernels and the pseudoeffectivity of relative canonical bundles
• Adiabatic limits of Ricci-flat Kähler metrics
• A gradient estimate in the Calabi-Yau theorem
• Positivity of direct image bundles and convexity on the space of Kähler metrics
• Unitary local systems, multiplier ideals, and polynomial periodicity of Hodge numbers
• Regularity properties of the degenerate Monge-Ampère equations on compact Kähler manifolds
• Heat kernel estimates and lower bound of eigenvalues
• The complex Monge-Ampère equation
• On rational singularities in dimensions \(>2\)
• Convergence of weak Kähler-Ricci flows on minimal models of positive Kodaira dimension
• Ohsawa-Takegoshi extension theorem for compact Kähler manifolds and applications
• Positivity of relative canonical bundles and applications
• Gaussian upper bounds for the heat kernels of some second-order operators on Riemannian manifolds
• Variation of singular Kähler-Einstein metrics: positive Kodaira dimension
• Families of conic Kähler-Einstein metrics
• Kähler forms for families of Calabi-Yau manifolds
• Approximation of weak geodesics and subharmonicity of Mabuchi energy
• Hölder continuous solutions to Monge-Ampère equations
• On projective varieties with nef anticanonical divisors
• Some remarks on Brauer groups of \(K3\) surfaces
• Canonical singular hermitian metrics on relative canonical bundles
• Positivity of twisted relative pluricanonical bundles and their direct images
• Geometric stability of the cotangent bundle and the universal cover of a projective manifold
• Lectures on K3 Surfaces
• Positivity of direct images of fiberwise Ricci-flat metrics on Calabi-Yau fibrations
• Remarks on the collapsing of torus fibered Calabi–Yau manifolds
• Minimal models and the Kodaira dimension of algebraic fiber spaces.
• Harmonic functions on complete riemannian manifolds
• Rational Singularities of Higher Dimensional Schemes
• On the ricci curvature of a compact kähler manifold and the complex monge-ampére equation, I
• Degeneration of algebraic manifolds and the spectrum of Laplacian
• Relative adjoint transcendental classes and Albanese maps of compact Kaehler manifolds with nef Ricci curvature
• The moduli b-divisor of an lc-trivial fibration
• ON THE VOLUME OF A LINE BUNDLE
• Metrics with cone singularities along normal crossing divisors and holomorphic tensor fields
• Sobolev and mean‐value inequalities on generalized submanifolds of Rⁿ
• THE SET OF MEASURES GIVEN BY BOUNDED SOLUTIONS OF THE COMPLEX MONGE–AMPÈRE EQUATION ON COMPACT KÄHLER MANIFOLDS

This page was built for publication: Variation of singular Kähler-Einstein metrics: Kodaira dimension zero (with an appendix by Valentino Tosatti)