CONIC SINGULARITIES METRICS WITH PRESCRIBED RICCI CURVATURE: GENERAL CONE ANGLES ALONG NORMAL CROSSING DIVISORS

摘要

Let X be a non-singular compact Kahler manifold, endowed with an effective divisor D = Sigma(1 - beta(kappa))Y-kappa having simple normal crossing support, and satisfying beta(kappa) is an element of (0, 1). The natural objects one has to consider in order to explore the differential geometric properties of the pair (X, D) are the so-called metrics with conic singularities. In this article, we complete our earlier work [CGP13] concerning the Mange -Ampere equations on (X, D) by establishing Laplacian and L-2,L-alpha,L-beta estimates for the solution of these equations regardless of the size of the coefficients 0 < beta(kappa) < 1. In particular, we obtain a general theorem concerning the existence and regularity of Kahler-Einstein metrics with conic singularities along a normal crossing divisor.