In this paper, I give a new construction of a K\"{ a}hler-Einstein metrics on a smooth projective variety with ample canonical bundle. This result can be generalized to the construction of a singular K\"{ a}hler-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 K\"{ a}hler-Einstein volume form have been considered.
Categories: math.AG math.DG