Notes on direct images of pluricanonical bundles

TL;DR

This paper extends Popa--Schnell's theorem on direct images of pluricanonical bundles to cases with non-globally generated ample line bundles and explores implications in positive characteristic settings.

Contribution

It provides a generalization of existing theorems to broader conditions and includes analysis in positive characteristic, expanding the applicability of the theory.

Findings

Generalized Popa--Schnell's theorem for non-globally generated line bundles

Extended results to positive characteristic cases

Enhanced understanding of direct images of pluricanonical bundles

Abstract

In this note, we generalize slightly Popa--Schnell's theorem regarding to direct images of pluricanonical bundles to the case when the ample line bundle is not globally generated. We also treat the case of positive characteristic.