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

Email:
fujino@math.kyoto-u.ac.jp

DOI:
https://doi.org/10.1090/S1056-3911-2010-00558-9

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