Degenerate complex Monge-Ampère equations over compact Kähler manifolds

Mathematics – Differential Geometry

Scientific paper

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The present manuscript expands and completes a paper accepted for publication in the International Journal of Mathematics, whi

Scientific paper

We prove the existence and uniqueness of the solutions of some very general
type of degenerate complex Monge-Amp\`ere equations. This type of equations is
precisely what is needed in order to construct K\"ahler-Einstein metrics over
irreducible singular K\"ahler spaces with ample or trivial canonical sheaf and
singular K\"ahler-Einstein metrics over varieties of general type.

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