Isometry group of Sasaki-Einstein metrics (Q2438566)

Let \((M,g)\) be a Sasaki-Einstein manifold, that is, its Kähler cone is a Calabi-Yau cone with Ricci flat metric. Let \((X,J)\) be the underlying affine variety of its Kähler cone and \(\operatorname{Aut}(X,J)\) denotes its automorphism group. In his main result the author proves a conjecture of Martelli-Sparks-Yau, regarding the isometry group of a Sasaki-Einstein metric. Namely, the identity component of the holomorphic isometry group of \((M,g)\) is the identity component of a maximal compact subgroup of \(\operatorname{Aut}(X,J)\).