Riemannian geometry of Kahler-Einstein currents II: an analytic proof of Kawamata's base point free theorem

Abstract

It is proved by Kawamata that the canonical bundle of a projective manifold is semi-ample if it is big and nef. We give an analytic proof using the Ricci flow, degeneration of Riemannian manifolds and $L^2$-theory. Combined with our earlier results, we construct unique singular Kahler-Einstein metrics with a global Riemannian structure on canonical models. Our approach can be viewed as the Kodaira embedding theorem on singular metric spaces with canonical Kahler metrics.

References in corpus (10)

• 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
• Kahler-Einstein metrics on Fano manifolds, II: limits with cone angle less than 2 π
• Kahler-Einstein metrics on Fano manifolds, I: approximation of metrics with cone singularities
• Riemannian geometry of Kahler-Einstein currents
• Ricci flow and birational surgery
• Degeneration of Kahler-Ricci solitons on Fano manifolds
• On the structure of almost Einstein manifolds

Cited by in corpus (8)

• Degeneration of Kahler-Einstein manifolds of negative scalar curvature
• Bounding diameter of singular Kähler metric
• Convergence of Kähler-Ricci flow on lower dimensional algebraic manifolds of general type
• On the Kahler Ricci flow on projective manifolds of general type
• Geometric estimates for complex Monge-Ampere equations
• Canonical metric on a mildly singular Kähler varieties with an intermediate log Kodaira dimension
• Bounding diameter of conical Kahler metric
• Generalized Kähler-Einstein metric along $\mathbb{Q}$-Fano fibration