2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/141267We 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 3.4Algebraic GeometryComplex Variables14J15text