Conic singularities metrics with prescribed Ricci curvature: General cone angles along normal crossing divisors

Let X be a non-singular compact Kähler manifold, endowed with an effective divisor D=∑(1-βₖ) Yₖ having simple normal crossing support, and satisfying βₖ ∈ (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 concerning the Monge-Ampère equations on $(X,D)$ by establishing Laplacian and C2,α,β estimates for the solution of these equations regardless of the size of the coefficients 0 < βₖ < 1. In particular, we obtain a general theorem concerning the existence and regularity of Kähler–Einstein metrics with conic singularities along a normal crossing divisor.