Canonical measures and Kahler-Ricci flow

Abstract

We show that the Kahler-Ricci flow on an algebraic manifold of positive Kodaira dimension and semi-ample canonical line bundle converges to a unique canonical metric on its canonical model. It is also shown that there exists a canonical measure of analytic Zariski decomposition on an algebraic manifold of positive Kodaira dimension. Such a canonical measure is unique and invariant under birational transformations under the assumption of the finite generation of canonical rings.

56 pages

References in corpus (5)

• Existence of minimal models for varieties of log general type
• Limits of Calabi-Yau metrics when the Kahler class degenerates
• A General Non-Vanishing Theorem and an Analytic Proof of the Finite Generation of the Canonical Ring
• Stability of Bounded Solutions for Degenerate Complex Monge-Ampère equations
• A priori $L^{\infty }$-estimates for degenerate complex Monge-Ampère equations