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A vanishing theorem of Koll'ar-Ohsawa type

Published 13 Nov 2015 in math.CV, math.AG, and math.DG | (1511.04222v3)

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 L2-method for the dbar-equation.

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