Vol. 6, No. 4, 2012

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ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Basepoint-free theorems: saturation, b-divisors, and canonical bundle formula

Osamu Fujino

Vol. 6 (2012), No. 4, 797–823
Abstract

We reformulate basepoint-free theorems using notions introduced by Shokurov, such as b-divisors and saturation of linear systems. Our formulation is flexible and has some important applications. One of the main purposes of this paper is to prove a generalization of the basepoint-free theorem in Fukuda’s paper “On numerically effective log canonical divisors”.

Keywords
basepoint-free theorem, canonical bundle formula, b-divisor, saturation
Mathematical Subject Classification 2010
Primary: 14C20
Secondary: 14N30, 14E30
Milestones
Received: 30 April 2011
Revised: 18 May 2011
Accepted: 20 June 2011
Published: 25 July 2012
Authors
Osamu Fujino
Department of Mathematics, Faculty of Science
Kyoto University
Sakyo-ku Kitashirakawa
Oiwake-cho, Kyoto 606-8502
Japan