Higher direct images of log canonical divisors and positivity theorems

Details Higher direct images of log canonical divisors and positivity theorems Higher direct images of log canonical divisors and positivity theorems

2003-02-07

arxiv.org/abs/math/0302073v1

Mathematics

Algebraic Geometry

38 pages, with Appendix by Morihiko Saito

Scientific paper

In this paper, we investigate higher direct images of log canonical divisors. After we reformulate Koll\'ar'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.

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