On the regularity of conical Calabi–Yau potentials
Volume 131 / 2023
Annales Polonici Mathematici 131 (2023), 21-56
MSC: Primary 32Q20; Secondary 32Q25, 35J96, 32U05, 32U20, 32U25, 32U35, 53C25.
DOI: 10.4064/ap221017-25-5
Published online: 11 September 2023
Abstract
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.
