On the Modified Futaki Invariant of Complete Intersections in Projective Spaces

Abstract

Abstract. Let M be a Fano manifold. We call a Kähler metric ω ∈ c1(M ) a Kähler-Ricci soliton if it satisfies the equation Ric(ω) − ω = LV ω for some holomorphic vector field V on M . It is known that a necessary condition for the existence of Kähler-Ricci solitons is the vanishing of the modified Futaki invariant introduced by Tian-Zhu. In a recent work of Berman-Nyström, it was generalized for (possibly singular) Fano varieties and the notion of algebro-geometric stability of the pair (M, V ) was introduced. In this paper, we propose a method of computing the modified Futaki invariant for Fano complete intersections in projective spaces.