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Article Dans Une Revue International Mathematics Research Notices Année : 2021

Continuity of singular Kähler-Einstein potentials

Résumé

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. We show that the associated singular Kähler-Einstein metrics are strictly positive when the variety is moreover smoothable.
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Dates et versions

hal-03039820 , version 1 (04-12-2020)
hal-03039820 , version 2 (06-10-2021)

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  • HAL Id : hal-03039820 , version 1

Citer

Vincent Guedj, Henri Guenancia, Ahmed Zeriahi. Continuity of singular Kähler-Einstein potentials. International Mathematics Research Notices, In press. ⟨hal-03039820v1⟩
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