Canonical measures and Kähler-Ricci flow

Song, Jian; Tian, Gang

doi:10.1090/S0894-0347-2011-00717-0

Canonical measures and Kähler-Ricci flow
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by Jian Song and Gang Tian

J. Amer. Math. Soc. 25 (2012), 303-353

DOI: https://doi.org/10.1090/S0894-0347-2011-00717-0

Published electronically: 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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