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 (4)

• 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

Cited by in corpus (9)

• Kahler-Einstein metrics on Fano manifolds, III: limits as cone angle approaches 2π and completion of the main proof
• The Ricci flow on the sphere with marked points
• Extremal Kähler metrics
• Riemannian geometry of Kahler-Einstein currents II: an analytic proof of Kawamata's base point free theorem
• Unnormalize conical Kähler-Ricci flow
• On the regularity problem of complex Monge-Ampere equations with conical singularities
• Regularity of Kähler-Ricci flow
• Orbifold regularity of weak Kahler-Einstein metrics
• $C^{2,\alpha }$-estimate for Monge-Ampere equations with Hölder-continuous right hand side