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On mixed-$\omega$-sheaves
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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.
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