Continuity of Monge–Ampère Potentials in Big Cohomology Classes

Quang-Tuan Dang (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

Abstract Extending Di Nezza–Lu’s approach [16] to the setting of big cohomology classes, we prove that solutions of degenerate complex Monge–Ampère equations on compact Kähler manifolds are continuous on a Zariski open set. This allows us to show that singular Kähler–Einstein metrics on log canonical varieties of general type have continuous potentials on the ample locus outside of the non-klt part.

Domains: Mathematics [math]

Quang-Tuan Dang. Continuity of Monge–Ampère Potentials in Big Cohomology Classes. International Mathematics Research Notices, 2021, ⟨10.1093/imrn/rnab183⟩. ⟨hal-03466536⟩