Injectivity theorems with multiplier ideal sheaves for higher direct images under Kähler morphisms

Abstract

In this paper, we establish injectivity theorems for higher direct image sheaves of canonical bundles twisted by pseudo-effective line bundles and multiplier ideal sheaves. As applications, we generalize Kollr's torsion-freeness and Grauert-Riemenschneider's vanishing theorem. Moreover, we obtain a relative vanishing theorem of Kawamata-Viehweg-Nadel type and an extension theorem for holomorphic sections from fibers of morphisms. Our approach, based on transcendental methods, works for Khler morphisms and singular Hermitian metrics with non-algebraic singularities.

Topics & Concepts