2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66463In 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.38 pages, with Appendix by Morihiko SaitoAlgebraic Geometry14N30; 14D07; 14J40; 14E30text