Multiplier ideal sheaves and existence of Kähler-Einstein metrics of positive scalar curvature

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RESUMO

To study C0a priori estimates for solutions to certain complex Monge—Ampère equations, I introduce a coherent sheaf of ideals and show that it satisfies various global algebrogeometric conditions, including a cohomology vanishing theorem. This technique is used to establish the existence of Kähler-Einstein metrics of positive scalar curvature on a very large class of compact complex manifolds.

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