Riemannian geometry of Kahler-Einstein currents
arXiv:1404.0445
Abstract
We study Riemannian geometry of canonical Kahler-Einstein currents on projective Calabi-Yau varieties and canonical models of general type with crepant singularities. We prove that the metric completion of the regular part of such a canonical current is a compact metric length space homeomorphic to the original projective variety, with well-defined tangent cones. We also prove a special degeneration for Kahler-Einstein manifolds of general type as an approach to establish the compactification of the moduli space of Kahler-Einstein manifolds of general type. A number of applications are given for degeneration of Calabi-Yau manifolds and the Kahler-Ricci flow on smooth minimal models of general type.
References in corpus (7)
- K-stability and Kähler-Einstein metrics
- Kahler-Einstein metrics on Fano manifolds, III: limits as cone angle approaches 2π and completion of the main proof
- The Kahler-Ricci flow through singularities
- Gromov-Hausdorff limits of Kahler manifolds and algebraic geometry, II
- Ricci flow and birational surgery
- Degeneration of Kahler-Ricci solitons on Fano manifolds
- On the structure of almost Einstein manifolds
Cited by in corpus (13)
- Gromov-Hausdorff limits of Kahler manifolds and algebraic geometry, II
- Collapsing behavior of Ricci-flat Kahler metrics and long time solutions of the Kahler-Ricci flow
- Degeneration of Kahler-Einstein manifolds of negative scalar curvature
- Riemannian geometry of Kahler-Einstein currents II: an analytic proof of Kawamata's base point free theorem
- Bounding diameter of singular Kähler metric
- The local entropy along Ricci flow---Part A: the no-local-collapsing theorems
- Convergence of Kähler-Ricci flow on lower dimensional algebraic manifolds of general type
- On the Kahler Ricci flow on projective manifolds of general type
- Diameter and Ricci curvature estimates for long-time solutions of the Kahler-Ricci flow
- A continuity method to construct canonical metrics
- Geometric estimates for complex Monge-Ampere equations
- The continuity equation with cusp singularities
- Bounding diameter of conical Kahler metric