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Nef anti-canonical divisors and rationally connected fibrations

Part of: Special varieties Families, fibrations

Published online by Cambridge University Press:  28 June 2019

Sho Ejiri  and
Yoshinori Gongyo
Sho Ejiri
Affiliation:
Department of Mathematics, Graduate School of Science, Osaka University Toyonaka, Osaka 560-0043, Japan email s-ejiri@cr.math.sci.osaka-u.ac.jp
Yoshinori Gongyo
Affiliation:
Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan email gongyo@ms.u-tokyo.ac.jp
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Abstract

We study the Iitaka–Kodaira dimension of nef relative anti-canonical divisors. As a consequence, we prove that given a complex projective variety with klt singularities, if the anti-canonical divisor is nef, then the dimension of a general fibre of the maximal rationally connected fibration is at least the Iitaka–Kodaira dimension of the anti-canonical divisor.

Keywords

anti-canonical divisorMRC fibration

MSC classification

Primary: 14D06: Fibrations, degenerations
Secondary: 14M22: Rationally connected varieties
Type
Research Article
Information
Compositio Mathematica , Volume 155 , Issue 7 , July 2019 , pp. 1444 - 1456
Copyright
© The Authors 2019 

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