Conic Kähler-Einstein metrics along simple normal crossing divisors on Fano manifolds

Abstract

We prove that on one Kähler-Einstein Fano manifold without holomorphic vector fields, there exists a unique conical Kähler-Einstein metric along a simple normal crossing divisor with admissible prescribed cone angles. We also establish a curvature estimate for conic metrics along a simple normal crossing divisor which generalizes Li-Rubinstein's estimate and derive high order estimates from this estimate.

arXiv commentarXiv admin note: text overlap with arXiv:1511.00183. Accepted by J. Func. Anal