Ricci iterations and canonical Kähler-Einstein currents on log canonical pairs

Abstract

In this article we construct a canonical Kähler-Einstein current on a LC (log canonical) pairs of log general type as the limit of a sequence of canonical Kähler-Einstein currents on KLT(Kawamata log terminal) pairs of log general type. We call the volume form associated with the canonical Kähler-Einstein current the canonical measure of the LC pair. We prove that the relative canonical measure on a projective family of LC pairs of log general type defines a singular hermitian metric on the relative log canonical bundle and the metric has semipositive curvature in the sense of current. This is the first semipositivity result for relative log canonical bundles of a family of LC pairs in general dimension. Our proof depends on certain Ricci iterations and dynamical systems of Bergman kernels.

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References in corpus (4)

• Existence of minimal models for varieties of log general type
• Curvature of vector bundles associated to holomorphic fibrations
• Canonical singular hermitian metrics on relative logcanonical bundles
• Dynamical construction of Kähler-Einstein metrics

Cited by in corpus (3)

• A thermodynamical formalism for Monge-Ampere equations, Moser-Trudinger inequalities and Kahler-Einstein metrics
• Canonical singular hermitian metrics on relative logcanonical bundles
• Global generation of the direct images of relative pluricanonical systems