Bando-Calabi-Futaki character of compact toric manifolds

Abstract

The Bando-Calabi-Futaki character of a compact Kähler manifold is an obstruction to the existence of Kähler metrics with constant scalar curvature, which is a generalization of the Futaki character of a Fano manifold. In this paper, we study the Bando-Calabi-Futaki character of a compact toric manifold. In particular, we shall prove that the Bando-Calabi-Futaki character of a compact toric manifold vanishes on the Lie algebra of the unipotent radical of the automorphism group.