On mixed-$\omega$-sheaves

TL;DR

This paper introduces mixed-$oldsymbol{ extomega}$-sheaves, generalizing Nakayama's $oldsymbol{ extomega}$-sheaves, to study a relative version of Fujita's freeness conjecture and its relation to the Iitaka conjecture, especially for log canonical pairs.

Contribution

It develops the theory of mixed-$oldsymbol{ extomega}$-sheaves, expanding Nakayama's framework, and applies it to problems in algebraic geometry related to Fujita's conjecture and log canonical pairs.

Findings

Generalization of Nakayama's $ extomega$-sheaves to mixed-$oldsymbol{ extomega}$-sheaves

Application to a relative version of Fujita's freeness conjecture

Insights into the Iitaka conjecture for log canonical pairs

Abstract

We introduce the notion of mixed-$\omega$-sheaves and use it for the study of a relative version of Fujita's freeness conjecture. It is related to the Iitaka conjecture. We note that the notion of mixed-$\omega$-sheaves is a generalization of that of Nakayama's $\omega$-sheaves in some sense. One of the main motivations of this paper is to make Nakayama's theory of $\omega$-sheaves more accessible and make it applicable to the study of log canonical pairs.