A polar dual to the momentum of toric Fano manifolds

Abstract

We introduce an invariant on the Fano polytope of a toric Fano manifold as a polar dual counterpart to the momentum of its polar dual polytope. Moreover, we prove that if the momentum of the polar dual polytope is equal to zero, then the dual invariant on a Fano polytope vanishes.

Keywords

• kähler-einstein metrics
• toric fano manifolds
• futaki invariant
• fano polytopes
• 14m25
• 14j45
• 32q20