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Canonical measures and Kähler-Ricci flow

Authors: Jian Song and Gang Tian
Journal: J. Amer. Math. Soc. 25 (2012), 303-353
MSC (2010): Primary 53-XX; Secondary 14-XX
Published electronically: October 12, 2011
MathSciNet review: 2869020
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Abstract: We show that the Kähler-Ricci flow on a projective 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 a projective 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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Additional Information

Jian Song
Affiliation: Department of Mathematics, Rutgers University, Piscataway, New Jersey 08854

Gang Tian
Affiliation: School of Mathematical Sciences and BICMR, Peking University, Beijing, 100871, People’s Republic of China and Department of Mathematics, Princeton University, Princeton, New Jersey 08544

Keywords: Ricci flow, Kähler-Einstein metrics, complex Monge-Ampère equations
Received by editor(s): November 25, 2008
Received by editor(s) in revised form: August 7, 2010
Published electronically: October 12, 2011
Additional Notes: This research is supported in part by National Science Foundation grants DMS-0604805 and DMS-0804095
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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