The Behavior of Multiplier Ideal Sheaves under Morphisms

Abstract

In [N1, N2] the author obtained the following theorem on the existence of Kähler-Einstein metrics of positive scalar curvature: Theorem Let M be a Fano manifold ¹ and let G ⊂ Aut(M) be a compact group of biholomorphisms and conjugate-bilolomorphisms of M. Assume that M does not admit a G-invariant multiplier ideal sheaf (in the sense of the definition below). Then M admits a Kähler-Einstein metric.