A remark on the decomposition theorem for direct images of canonical sheaves tensorized with semipositive vector bundles

Abstract

The purpose of this short note is to give a remark on the decomposition theorem for direct images of canonical sheaves tensorized with Nakano semipositive vector bundles. Although our result is a direct consequence of Takegoshi’s work in [3], it was not stated explicitly in [3]. Here we give the precise statement and the proof.