Canonical measures and Kähler-Ricci flow

Song, Jian¹ ; Tian, Gang²

¹ Department of Mathematics, Rutgers University, Piscataway, New Jersey 08854
² 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

Journal of the American Mathematical Society, Tome 25 (2012) no. 2, pp. 303-353

Résumé

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.

Détail

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

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