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Log pluricanonical representations and the abundance conjecture

Part of:Birational geometry

Published online by Cambridge University Press:  10 March 2014

Osamu Fujino and
Yoshinori Gongyo
Osamu Fujino
Affiliation:
Department of Mathematics, Faculty of Science, Kyoto University, Kyoto 606-8502, Japan email fujino@math.kyoto-u.ac.jp
Yoshinori Gongyo
Affiliation:
Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo 153-8914, Japan email gongyo@ms.u-tokyo.ac.jp email y.gongyo@imperial.ac.uk
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Abstract

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We prove the finiteness of log pluricanonical representations for projective log canonical pairs with semi-ample log canonical divisor. As a corollary, we obtain that the log canonical divisor of a projective semi log canonical pair is semi-ample if and only if the log canonical divisor of its normalization is semi-ample. We also treat many other applications.

Keywords

pluricanonical representationabundance conjectureminimal model program

MSC classification

Secondary:14E30: Minimal model program (Mori theory, extremal rays)14E07: Birational automorphisms, Cremona group and generalizations

Information

Type
Research Article
Information
Compositio Mathematica , Volume 150 , Issue 4 , April 2014, pp. 593 - 620
Copyright
© The Author(s) 2014 

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