Continuity of Monge-Amp\`ere Potentials in Big Cohomology Classes
Abstract
Extending DiNezza-Lu's approach to the setting of big cohomology classes, we prove that solutions of degenerate complex Monge-Amp\`ere equations on compact K\"ahler manifolds are continuous on a Zariski open set. This allows us to show that singular K\"ahler-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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