Dynamical construction of Kähler-Einstein metrics

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 morphismf:X→Swith connected fibers such that a general fiber has an ample canonical bundle, and for a positive integerm, we construct a canonical singular Hermitian metrichE,monwith semipositive curvature in the sense of Nakano.

Dynamical construction of Kähler-Einstein metrics

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: X → 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 hE,m on with semipositive curvature in the sense of Nakano.