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

Abstract

To study C ⁰ a 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.

• Monge—Ampère equation
• coherent sheaf
• cohomology
• a priori estimate