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 $\omega$-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.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2014
- DOI:
- 10.48550/arXiv.1406.2759
- arXiv:
- arXiv:1406.2759
- Bibcode:
- 2014arXiv1406.2759F
- Keywords:
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- Mathematics - Algebraic Geometry;
- 14R05 (Primary);
- 14E30 (Secondary)
- E-Print:
- 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