Kähler-Einstein metrics with cone singularities on klt pairs

Abstract

Let (X,D) be a klt pair. Assuming either K_X+D big or -(K_X+D) ample, and that the coefficients of D are greater than 1/2, we show that the Kähler-Einstein metric attached to (X,D) -whenever it exists- has cone singularities along D on the log-smooth locus of the pair intersected with the ample locus of K_X+D (in the negatively curved case).

19 pages

References in corpus (2)

• A variational approach to complex Monge-Ampere equations
• Regularity properties of the degenerate Monge--Ampère equations compact Kähler manifolds