On the regularity of conical Calabi-Yau potentials

Using pluripotential theory on degenerate Sasakian manifolds, we show that a locally bounded conical Calabi-Yau potential on a Fano cone is actually smooth on the regular locus. This work is motivated by a similar result obtained by R. Berman in the case where the cone is toric. Our proof is purely...

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Bibliographic Details
Published in:arXiv.org 2023-05
Main Author: Tran-Trung Nghiem
Format: Article
Language:English
Online Access:Get full text
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Summary:Using pluripotential theory on degenerate Sasakian manifolds, we show that a locally bounded conical Calabi-Yau potential on a Fano cone is actually smooth on the regular locus. This work is motivated by a similar result obtained by R. Berman in the case where the cone is toric. Our proof is purely pluripotential and independent of any extra symmetry imposed on the cone.
ISSN:2331-8422