Degenerate complex Monge-Ampère equations over compact Kähler manifolds
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We prove the existence and uniqueness of the solutions of some very general type of degenerate complex Monge-Ampère equations. This type of equations is precisely what is needed in order to construct Kähler-Einstein metrics over irreducible singular Kähler spaces with ample or trivial canonical sheaf and singular Kähler-Einstein metrics over varieties of general type.
The present manuscript expands and completes a paper accepted for publication in the International Journal of Mathematics, which had to be shortened in view of the length of the manuscript and of the demands of referees - in particular it gives more details about the relation with the existing litterature (see Appendix C)
The present manuscript expands and completes a paper accepted for publication in the International Journal of Mathematics, which had to be shortened in view of the length of the manuscript and of the demands of referees - in particular it gives more details about the relation with the existing litterature (see Appendix C)