Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



Non-vanishing theorem for log canonical pairs

Author: Osamu Fujino
Journal: J. Algebraic Geom. 20 (2011), 771-783
Published electronically: January 3, 2011
MathSciNet review: 2819675
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Abstract | References | Additional Information

Abstract: We obtain a correct generalization of Shokurov's non-vanishing theorem for log canonical pairs. It implies the base point free theorem for log canonical pairs. We also prove the rationality theorem for log canonical pairs. As a corollary, we obtain the cone theorem for log canonical pairs. We do not need Ambro's theory of quasi-log varieties.

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Additional Information

Osamu Fujino
Affiliation: Department of Mathematics, Faculty of Science, Kyoto University, Kyoto 606-8502 Japan

Received by editor(s): March 23, 2009
Received by editor(s) in revised form: December 1, 2009
Published electronically: January 3, 2011
Additional Notes: The author was partially supported by The Inamori Foundation and by the Grant-in-Aid for Young Scientists (A) $♯$20684001 from JSPS

American Mathematical Society