Kahler-Einstein metrics on Fano manifolds, II: limits with cone angle less than 2 π

Abstract

This is the second of a series of three papers which provide proofs of results announced in arXiv:1210.7494. In this paper we consider the Gromov-Hausdorff limits of metrics with cone singularities in the case when the limiting cone angle is less than 2π. We show that these are in a natrual way projective algebraic varieties. In the case when the limiting variety and the limiting divisor are smooth we show that the limiting metric also has standard cone singularities.

References in corpus (5)

• Gromov-Hausdorff limits of Kahler manifolds and algebraic geometry, II
• Singular Kahler-Einstein metrics
• Kahler-Einstein metrics and stability
• Ricci flat Kahler metrics with edge singularities
• Geodesics in the space of Kähler cone metrics

Cited by in corpus (31)

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• Special test configurations and $K$-stability of Fano varieties
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• Conic singularities metrics with prescribed Ricci curvature: the case of general cone angles along normal crossing divisors
• Bessel Functions, Heat Kernel and the Conical Kähler-Ricci Flow
• Smooth approximations of the Conical Kahler-Ricci flows
• The conical Kähler-Ricci flow on Fano manifolds
• Geodesics in the space of Kähler cone metrics
• On the long time behaviour of the Conical Kähler- Ricci flows
• The Ricci flow on the sphere with marked points
• Extremal Kähler metrics
• Connecting toric manifolds by conical Kahler-Einstein metrics
• A remark on Kahler metrics with conical singularities along a simple normal crossing divisor
• 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
• Alpha-invariant of Toric Line Bundles
• $C^{2,\alpha }$-estimate for conical Kähler-Ricci flow
• Scalar curvature and Futaki invariant of Kähler metrics with cone singularities along a divisor
• On the regularity problem of complex Monge-Ampere equations with conical singularities
• Regularity of Kähler-Ricci flow
• Alpha invariants and K-stability for general polarisations of Fano varieties
• Note on Poincaré type Kähler metrics and Futaki characters
• On convexity of the regular set of conical Kahler-Einstein metrics
• Orbifold regularity of weak Kahler-Einstein metrics
• Interior Estimates for the $n$-dimensional Abreu's Equation
• $C^{2,\alpha }$-estimate for Monge-Ampere equations with Hölder-continuous right hand side
• Toric partial density functions and stability of toric varieties