## Nagoya Mathematical Journal

### Dynamical construction of Kähler-Einstein metrics

Hajime Tsuji

#### Abstract

In this article, we give a new construction of a Kähler-Einstein metric on a smooth projective variety with ample canonical bundle. As a consequence, for a dominant projective morphism $f\dvtx X\longrightarrow S$ with connected fibers such that a general fiber has an ample canonical bundle, and for a positive integer $m$, we construct a canonical singular Hermitian metric $h_{E,m}$ on $f_{*}{\mathcal O}_{X}(mK_{X/S})$ with semipositive curvature in the sense of Nakano.

#### Article information

Source
Nagoya Math. J., Volume 199 (2010), 107-122.

Dates
First available in Project Euclid: 14 September 2010

https://projecteuclid.org/euclid.nmj/1284471572

Digital Object Identifier
doi:10.1215/00277630-2010-005

Mathematical Reviews number (MathSciNet)
MR2730413

Zentralblatt MATH identifier
1205.32021

#### Citation

Tsuji, Hajime. Dynamical construction of Kähler-Einstein metrics. Nagoya Math. J. 199 (2010), 107--122. doi:10.1215/00277630-2010-005. https://projecteuclid.org/euclid.nmj/1284471572

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