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 pluripotential and independent of any extra symmetry imposed on the cone.