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