Higher direct images of log canonical divisors

Abstract

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. The final section is an appendix, which is a result of Morihiko Saito. © 2003 Applied Probability Trust.