Toric Sasaki–Einstein metrics with conical singularities

Abstract We show that any toric Kähler cone with smooth compact cross-section admits a family of Calabi–Yau metrics conical singularities along its divisors. The is parametrized by the Reeb and angles are given explicitly in terms vector field. result optimal, sense metric divisor (and elsewhere) belongs to this family. also provide examples interpret our results Sasaki–Einstein metrics.