K-stability and Kähler-Einstein metrics

Abstract

In this new version, we correct some typos. For the readers' convenience, we also added some footnotes and more details for certain lemmas and theorems.

47 pages

References in corpus (7)

• A Brunn-Minkowski type inequality for Fano manifolds and the Bando-Mabuchi uniqueness theorem
• Gromov-Hausdorff limits of Kahler manifolds and algebraic geometry, II
• Special test configurations and $K$-stability of Fano varieties
• Conical Kahler-Einstein metric revisited
• Ricci flat Kahler metrics with edge singularities
• Remarks on logarithmic K-stability
• Note on K-stability of pairs

Cited by in corpus (46)

• Asymptotics of spectral function of lower energy forms and Bergman kernel of semi-positive and big line bundles
• Complex optimal transport and the pluripotential theory of Kähler-Ricci solitons
• Special test configurations and $K$-stability of Fano varieties
• Birationally rigid Fano threefold hypersurfaces
• On the moduli of Kahler-Einstein Fano manifolds
• Optimal bounds for the volumes of Kähler-Einstein Fano manifolds
• Kähler-Einstein metrics on group compactifications
• Asymptotically log Fano varieties
• Riemannian geometry of Kahler-Einstein currents
• Positive scalar curvature with skeleton singularities
• Conic singularities metrics with prescribed Ricci curvature: the case of general cone angles along normal crossing divisors
• The conical Kähler-Ricci flow on Fano manifolds
• The Ricci flow on the sphere with marked points
• Yau-Tian-Donaldson correspondence for K-semistable Fano manifolds
• Stable Pairs and Coercive Estimates for The Mabuchi Functional
• Connecting toric manifolds by conical Kahler-Einstein metrics
• Quasi-projectivity of the moduli space of smooth Kahler-Einstein Fano manifolds
• Regularity of Kähler-Ricci flows on Fano manifolds
• Riemannian geometry of Kahler-Einstein currents II: an analytic proof of Kawamata's base point free theorem
• Unnormalize conical Kähler-Ricci flow
• Homogeneous Einstein metrics on Euclidean spaces are Einstein solvmanifolds
• Bounding diameter of singular Kähler metric
• Alpha-invariant of Toric Line Bundles
• Compact moduli space of Kahler-Einstein Fano varieties
• Ricci de Turck flow on singular manifolds
• $C^{2,\alpha }$-estimate for conical Kähler-Ricci flow
• Properness of log $F$-functionals
• Regularity of Kähler-Ricci flow
• Examples of K-unstable Fano manifolds with the Picard number one
• Alpha invariants and K-stability for general polarisations of Fano varieties
• Stability of tangent bundle on the moduli space of stable bundles on a curve
• On convexity of the regular set of conical Kahler-Einstein metrics
• On the uniform K-stability for some asymptotically log del Pezzo surfaces
• Orbifold regularity of weak Kahler-Einstein metrics
• On the modified Futaki invariant of complete intersections in projective spaces
• A decomposition formula for J-stability and its applications
• Fano manifolds with weak almost Kähler-Ricci solitons
• Interior Estimates for the $n$-dimensional Abreu's Equation
• Kähler-Einstein metrics and higher alpha-invariants
• Twisted and conical Kähler-Ricci soliton on Fano manifolds
• An extremal eigenvalue problem in Kähler geometry
• Toric partial density functions and stability of toric varieties
• Cohomology formula for obstructions to asymptotic Chow semistability
• Generalized Kähler-Einstein metric along $\mathbb{Q}$-Fano fibration
• Bounding diameter of conical Kahler metric
• Calabi problem for manifolds with edge-cone singularities