English

A vanishing theorem of Koll'ar-Ohsawa type

Complex Variables 2018-01-29 v3 Algebraic Geometry Differential Geometry

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.

Keywords

Cite

@article{arxiv.1511.04222,
  title  = {A vanishing theorem of Koll'ar-Ohsawa type},
  author = {Shin-ichi Matsumura},
  journal= {arXiv preprint arXiv:1511.04222},
  year   = {2018}
}

Comments

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