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Continuity of Monge–Ampère Potentials in Big Cohomology Classes

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.
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Submitted on : Monday, December 6, 2021 - 12:54:24 AM
Last modification on : Monday, July 4, 2022 - 9:48:36 AM

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



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