A vanishing theorem of Koll'ar-Ohsawa type

Abstract

For proper surjective holomorphic maps from K"ahler manifolds to analytic spaces, we give a decomposition theorem for the cohomology groups of the canonical bundle twisted by Nakano semi-positive vector bundles by means of the higher direct image sheaves, by using the theory of harmonic integrals developed by Takegoshi. As an application, we prove a vanishing theorem of Koll'ar-Ohsawa type by combining the L^2-method for the dbar-equation.

14pages, v2: the title was changed, Theorem 1.3 was slightly generalized, v3: completely revised version

References in corpus (2)

• On semipositivity, injectivity and vanishing theorems
• A remark on the decomposition theorem for direct images of canonical sheaves tensorized with semipositive vector bundles

Cited by in corpus (4)

• On semipositivity, injectivity and vanishing theorems
• A remark on the decomposition theorem for direct images of canonical sheaves tensorized with semipositive vector bundles
• Vanishing and semipositivity theorems for semi-log canonical pairs
• Global generation and very ampleness for adjoint linear series