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Article Dans Une Revue International Mathematics Research Notices Année : 2023

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.
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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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Vincent Guedj, Henri Guenancia, Ahmed Zeriahi. Continuity of singular Kähler-Einstein potentials. International Mathematics Research Notices, 2023, 2023 (2), pp.1355-1377. ⟨10.1093/imrn/rnab294⟩. ⟨hal-03039820v2⟩
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