2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/125599In this paper, I give a new construction of a Kähler-Einstein metrics on a smooth projective variety with ample canonical bundle. This result can be generalized to the construction of a singular Kähler-Einstein metric on a smooth projective variety of general type which gives an AZD of the canonical bundle. Also the variation of Bergman kernels and Kähler-Einstein volume form have been considered.25pages, no figure, Proof of Lemma 3.6 has been replaced by a result of Bedford and TaylorAlgebraic GeometryDifferential Geometry53C25, 32G07text