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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Canonical measures and Kähler-Ricci flow
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by Jian Song and Gang Tian PDF
J. Amer. Math. Soc. 25 (2012), 303-353 Request permission

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
  • Email: jiansong@math.rutgers.edu
  • 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
  • MR Author ID: 220655
  • Email: tian@math.princeton.edu
  • 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
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: J. Amer. Math. Soc. 25 (2012), 303-353
  • MSC (2010): Primary 53-XX; Secondary 14-XX
  • DOI: https://doi.org/10.1090/S0894-0347-2011-00717-0
  • MathSciNet review: 2869020