A generalization of Takegoshi's relative vanishing theorem

TL;DR

This paper extends Takegoshi's relative vanishing theorem to Nakano semi-positive sheaves on singular spaces, providing new insights into proper modifications of torsion-free sheaves.

Contribution

It generalizes Takegoshi's theorem to a broader class of sheaves and singular spaces, introducing new results on proper modifications.

Findings

Extended vanishing theorem to Nakano semi-positive sheaves

Established new results on proper modifications of torsion-free sheaves

Applicable to singular complex spaces

Abstract

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.