Higher direct images of log canonical divisors and positivity theorems
Algebraic Geometry
2007-05-23 v1
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. 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.
Keywords
Cite
@article{arxiv.math/0302073,
title = {Higher direct images of log canonical divisors and positivity theorems},
author = {Osamu Fujino},
journal= {arXiv preprint arXiv:math/0302073},
year = {2007}
}
Comments
38 pages, with Appendix by Morihiko Saito