On the modified Futaki invariant of complete intersections in projective spaces

Abstract

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 (singular) Fano varieties and the notion of algebro-geometric stability of the pair $(M,V)$ of a Fano manifold $M$ and a holomorphic vector field $V$ was introduced. In this paper, we propose a method of computing the modified Futaki invariant for Fano complete intersections in projective spaces.

17 pages, final version, to appear in Nagoya Mathematical Journal

References in corpus (5)

• K-stability and Kähler-Einstein metrics
• Kahler-Einstein metrics on Fano manifolds, III: limits as cone angle approaches 2π and completion of the main proof
• Complex optimal transport and the pluripotential theory of Kähler-Ricci solitons
• Modified Futaki invariant and equivariant Riemann-Roch formula
• A note on the holomorphic invariants of Tian-Zhu