Kähler-Einstein metrics: old and new

DOI10.1515/coma-2017-0014zbMath1457.53003arXiv1710.05380OpenAlexW3102039903MaRDI QIDQ680314

Cristiano Spotti, Daniele Angella

Publication date: 23 January 2018

Published in: Complex Manifolds (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1710.05380

zbMATH Keywords

Kähler-EinsteinFanoK-stabilityYau-Tian-Donaldson conjecturemoduli of Kähler-Einstein

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Kähler-Einstein manifolds (32Q20) Research exposition (monographs, survey articles) pertaining to differential geometry (53-02)

Related Items (2)

Equivariant stable sheaves and toric GIT ⋮ Constant \(\mu \)-scalar curvature Kähler metric -- formulation and foundational results

Cites Work

• K-polystability of Q-Fano varieties admitting Kähler-Einstein metrics
• Kähler-Einstein metrics along the smooth continuity method
• Conical Kähler-Einstein metrics revisited
• Gromov-Hausdorff limits of Kähler manifolds and algebraic geometry
• The Monge-Ampère equation and its applications
• Degenerate complex Monge-Ampère equations
• Greatest lower bounds on Ricci curvature for toric Fano manifolds
• Complex Monge-Ampère equations and geodesics in the space of Kähler metrics. Lecture notes
• On Calabi's conjecture for complex surfaces with positive first Chern class
• Complex analytic coordinates in almost complex manifolds
• On compact Kähler manifolds with positive definite Ricci tensor
• Réduction du cas positif de l'équation de Monge-Ampère sur les variétés Kählériennes compactes à la démonstration d'une inégalité
• Toric geometry, Sasaki-Einstein manifolds and a new infinite class of AdS/CFT duals
• On a set of polarized Kähler metrics on algebraic manifolds
• Log canonical thresholds of del Pezzo surfaces
• K-stability of constant scalar curvature Kähler manifolds
• A functional integrating Futaki's invariant
• On Kähler-Einstein metrics on certain Kähler manifolds with \(C_ 1(M)>0\)
• Infinite determinants, stable bundles and curvature
• Some symplectic geometry on compact Kähler manifolds. I
• Remarks on the existence problem of positive Kähler-Einstein metrics
• Projective manifolds with ample tangent bundles
• Complete Kähler manifolds with zero Ricci curvature. II
• Rational connectedness and boundedness of Fano manifolds
• Real homotopy theory of Kähler manifolds
• Stability of projective varieties
• Lectures on introduction to moduli problems and orbit spaces
• Canonical coordinates and Bergmann metrics
• Extremal Kähler metrics and complex deformation theory
• Kähler-Einstein metrics with positive scalar curvature
• Scalar curvature and projective embeddings. I
• Elliptic partial differential equations of second order
• The space of Kähler metrics.
• Explicit Gromov-Hausdorff compactifications of moduli spaces of Kähler-Einstein Fano manifolds
• Minimizing normalized volumes of valuations
• On the \(C^{1,1}\) regularity of geodesics in the space of Kähler metrics
• Gromov-Hausdorff limits of Kähler manifolds and algebraic geometry. II
• Kähler-Einstein metrics on \(\mathbb{Q}\)-smoothable Fano varieties, their moduli and some applications
• Scalar curvature and stability of toric varieties.
• An obstruction to the existence of Einstein Kaehler metrics
• Holomorphic discs and the complex Monge-Ampère equation.
• Kähler--Ricci solitons on toric manifolds with positive first Chern class
• Complex geometry. An introduction
• Complex manifolds and deformation of complex structures. Transl. from the Japanese by Kazuo Akao
• The K-energy on hypersurfaces and stability
• Special test configuration and \(K\)-stability of Fano varieties
• Kähler-Einstein metrics: from cones to cusps
• Geodesics in the space of Kähler metrics
• Weak geodesics in the space of Kähler metrics
• Uniqueness of \(\mathbb{CP}^n\)
• A valuative criterion for uniform K-stability of \(\mathbb{Q}\)-Fano varieties
• A thermodynamical formalism for Monge-Ampère equations, Moser-Trudinger inequalities and Kähler-Einstein metrics
• Einstein manifolds
• Multiplier ideal sheaves and the Kähler-Ricci flow
• Lower bounds on the Calabi functional
• Lectures on Kähler manifolds
• Holomorphic vector fields and Kaehler manifolds
• The group of isometries of a Riemannian manifold
• On Kähler varieties of restricted type. (An intrinsic characterization of algebraic varieties.)
• Semi-continuity of complex singularity exponents and Kähler–Einstein metrics on Fano orbifolds
• Algebraic families of constant scalar curvature K\"ahler metrics
• Greatest lower bounds on the Ricci curvature of Fano manifolds
• Singular Kähler-Einstein metrics
• Sur les variétés analytiques complexes
• Sur la Structure du Groupe d’Homéomorphismes Analytiques d’une Certaine Variété Kaehlérinne
• A study of the Hilbert-Mumford criterion for the stability of projective varieties
• Kähler–Einstein Metrics and Stability
• Differential Analysis on Complex Manifolds
• Log canonical thresholds of smooth Fano threefolds
• An Algebraic Surface with K Ample, (K 2 ) = 9, p g = q = 0
• HOLOMORPHIC TENSORS AND VECTOR BUNDLES ON PROJECTIVE VARIETIES
• Classical solutions of fully nonlinear, convex, second-order elliptic equations
• Three dimensional manifolds, Kleinian groups and hyperbolic geometry
• ON STABILITY OF THE TANGENT BUNDLES OF FANO VARIETIES
• Complex Monge-Ampere and Symplectic Manifolds
• Calabi's conjecture and some new results in algebraic geometry
• On the ricci curvature of a compact kähler manifold and the complex monge-ampére equation, I
• Geometric Invariant Theory
• Optimal bounds for the volumes of Kähler-Einstein Fano manifolds
• K-STABILITY OF FANO MANIFOLDS WITH NOT SMALL ALPHA INVARIANTS
• On the existence of hermitian-yang-mills connections in stable vector bundles
• On the lower order terms of the asymptotic expansion of Tian-Yau-Zelditch
• A variational approach to the Yau–Tian–Donaldson conjecture
• Remarks on logarithmic K-stability
• Kähler Metrics with Cone Singularities Along a Divisor
• Convexity of the 𝐾-energy on the space of Kähler metrics and uniqueness of extremal metrics
• Kähler-Einstein metrics on Fano manifolds. III: Limits as cone angle approaches \boldmath2𝜋 and completion of the main proof
• On the Volume Elements on a Manifold
• ON THE CHERN NUMBERS OF CERTAIN COMPLEX AND ALMOST COMPLEX MANIFOLDS
• Complete Kahler Manifolds with Zero Ricci Curvature. I
• Vector fields and Ricci curvature
• On the Chern numbers of surfaces of general type
• Higher-dimensional algebraic geometry
• Lectures on symplectic geometry
• Kähler-Einstein metrics with edge singularities
• Compact moduli spaces of del Pezzo surfaces and Kähler-Einstein metrics
• 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
• 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
• Unnamed Item
• Unnamed Item

This page was built for publication: Kähler-Einstein metrics: old and new