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ISSN 1088-6834(e) ISSN 0894-0347(p)

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
Posted: October 12, 2011
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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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