Continuity of Singular Kähler–Einstein Potentials

Abstract In this note, we investigate some regularity aspects for solutions of degenerate complex Monge–Ampère equations (DCMAE) on singular spaces. First, study the Dirichlet problem DCMAE Stein spaces, showing a general continuity result. A consequence our results is that Kähler–Einstein potentials are continuous at isolated singularities. Next, establish global to when reference class belongs real Néron–Severi group. This yields in particular any irreducible Calabi–Yau variety.