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

摘要

The purpose of this short note is to give a remark on the decompositiontheorem for direct images of canonical sheaves tensorized with Nakanosemipositive vector bundles. Although our result is a direct consequence ofTakegoshi's work, it was not stated explicitly in his article. Here we give theprecise statement and the proof.