A vanishing theorem of Kollár–Ohsawa type

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For proper surjective holomorphic maps from Kähler 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 Kollár–Ohsawa type by combining the L2-method for the ∂¯ -equation.

Original languageEnglish
Pages (from-to)1451-1465
Number of pages15
JournalMathematische Annalen
Issue number3-4
Publication statusPublished - 2016 Dec 1


  • 58A14
  • Primary 32L20
  • Secondary 14C30


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