Higher direct images of log canonical divisors and positivity theorems

Abstract

In this paper, we investigate higher direct images of log canonical divisors. After we reformulate Kollár's torsion-free theorem, we treat the relationship between higher direct images of log canonical divisors and the canonical extensions of Hodge filtration of gradedly polarized variations of mixed Hodge structures. As a corollary, we obtain a logarithmic version of Fujita-Kawamata's semi-positivity theorem. By this semi-positivity theorem, we generalize Kawamata's positivity theorem and apply it to the study of a log canonical bundle formula. The final section is an appendix, which is a result of Morihiko Saito.

arXiv comment38 pages, with Appendix by Morihiko Saito

References in corpus (1)

• Quasi-log varieties

Cited by in corpus (6)

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• Remarks on log Calabi--Yau structure of varieties admitting polarized endomorphism
• Remarks on very basic slc-trivial fibrations