Canonical measures and Kahler-Ricci flow

Details Canonical measures and Kahler-Ricci flow Canonical measures and Kahler-Ricci flow

2008-02-19

arxiv.org/abs/0802.2570v1

Mathematics

Differential Geometry

56 pages

Scientific paper

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.

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