Advanced Studies in Pure Mathematics

Log Kodaira dimension of homogeneous varieties

Michel Brion and De-Qi Zhang

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Let $V$ be a complex algebraic variety, homogeneous under the action of a complex algebraic group. We show that the log Kodaira dimension of $V$ is non-negative if and only if $V$ is a semi-abelian variety.

Article information

Algebraic Varieties and Automorphism Groups, K. Masuda, T. Kishimoto, H. Kojima, M. Miyanishi and M. Zaidenberg, eds. (Tokyo: Mathematical Society of Japan, 2017), 1-6

Received: 24 July 2015
Revised: 3 November 2015
First available in Project Euclid: 21 September 2018

Permanent link to this document euclid.aspm/1537498702

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14M17: Homogeneous spaces and generalizations [See also 32M10, 53C30, 57T15]
Secondary: 14J50: Automorphisms of surfaces and higher-dimensional varieties 14L10: Group varieties 32M12: Almost homogeneous manifolds and spaces [See also 14M17]

Log Kodaira dimension homogeneous variety semi-abelian variety


Brion, Michel; Zhang, De-Qi. Log Kodaira dimension of homogeneous varieties. Algebraic Varieties and Automorphism Groups, 1--6, Mathematical Society of Japan, Tokyo, Japan, 2017. doi:10.2969/aspm/07510001.

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