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Journal Articles International Mathematics Research Notices Year : 2021

Continuity of Monge–Ampère Potentials in Big Cohomology Classes

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Abstract

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.

Dates and versions

hal-03466536 , version 1 (06-12-2021)

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