Canonical singular hermitian metrics on relative canonical bundles

Abstract

We introduce a new class of canonical AZD's (called the supercanonical AZD's) on the canonical bundles of smooth projective varieties with pseudoeffective canonical classes. We study the variation of the supercanonical AZD ${\hat{h}}_{can}$ under projective deformations and give a new proof of the invariance of plurigenera.

Correction on the proof of Lemma 3.2 and Corollary 3.4