A Generalization of Takegoshi’s Relative Vanishing Theorem

Journal article, 2016

We present a generalization of Takegoshi’s relative version of the Grauert–Riemenschneider vanishing theorem. Under some natural assumptions, we extend Takegoshi’s vanishing theorem to the case of Nakano semi-positive coherent analytic sheaves on singular complex spaces. We also obtain some new results about proper modifications of torsion-free coherent analytic sheaves.