On subadditivity of the logarithmic Kodaira dimension
Abstract
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 -sheaves and -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.
Keywords
Cite
@article{arxiv.1406.2759,
title = {On subadditivity of the logarithmic Kodaira dimension},
author = {Osamu Fujino},
journal= {arXiv preprint arXiv:1406.2759},
year = {2016}
}
Comments
18 pages, v2: Corollary 1.5, which is obviously wrong, was removed, v3: title changed, various revisions, v4: minor revisions, v5: minor revisions, v6: very minor revisions, v7: very minor revisions following referee's comments, v8: Theorem 1.9, Lemma 2.8, and Remark 3.8 are new. some mistakes are corrected