On the modified ideal sheaf

TL;DR

This paper extends the concept of modified ideal sheaves to analyze the asymptotic behavior of cohomology groups and explores their application in studying direct images of pseudo-effective line bundles.

Contribution

It generalizes the notion of modified ideal sheaves and applies it to the study of direct images of pseudo-effective line bundles.

Findings

Provides a broader theoretical framework for modified ideal sheaves.

Establishes new asymptotic estimates for cohomology groups.

Analyzes the properties of direct images in the context of pseudo-effective line bundles.

Abstract

It is a sequel to (Wu in arXiv:2003.05187). In that paper, we introduce a notion called modified ideal sheaf in order to make an asymptotic estimate for the order of the cohomology group. Here we continue to a general discussion about this notion. As an application, we study the direct images associated with a pseudo-effective line bundle.