An Upper Bound on the Critical Volume in a Class of Toric Sasaki-Einstein Manifolds

Understand

We prove the existence of an upper bound on critical volume of a large class of toric Sasaki-Einstein manifolds with respect to the first Chern class of the resolutions of the Gorenstein singularities in the corresponding toric Calabi-Yau varieties.

• We examine the canonical metrics obtained by the Delzant construction on these varieties and characterise cases when the bound is attained.
• We comment on computational tools used in the investigation, in particular Neural Networks and the gradient saliency method.