Open Access
October, 2017 On subadditivity of the logarithmic Kodaira dimension
J. Math. Soc. Japan 69(4): 1565-1581 (October, 2017). DOI: 10.2969/jmsj/06941565


We reduce Iitaka's subadditivity conjecture for the logarithmic Kodaira dimension to a special case of the generalized abundance conjecture by establishing an Iitaka type inequality for Nakayama's numerical Kodaira dimension. Our proof heavily depends on Nakayama's theory of $\omega$-sheaves and $\widehat{\omega}$-sheaves. As an application, we prove the subadditivity of the logarithmic Kodaira dimension for affine varieties by using the minimal model program for projective klt pairs with big boundary divisor.


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Osamu FUJINO. "On subadditivity of the logarithmic Kodaira dimension." J. Math. Soc. Japan 69 (4) 1565 - 1581, October, 2017.


Published: October, 2017
First available in Project Euclid: 25 October 2017

zbMATH: 06821652
MathSciNet: MR3715816
Digital Object Identifier: 10.2969/jmsj/06941565

Primary: 14R05
Secondary: 14E30

Keywords: $\omega$-sheaf , $\widehat \omega$-sheaf , abundance conjecture , affine varieties , Iitaka conjecture , logarithmic Kodaira dimension , minimal model program , Nakayama's numerical Kodaira dimension

Rights: Copyright © 2017 Mathematical Society of Japan

Vol.69 • No. 4 • October, 2017
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