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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2312.04015 |
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| _version_ | 1866917621342928896 |
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| author | Chang, Chi-Kang |
| author_facet | Chang, Chi-Kang |
| contents | In this article, we will prove the Generalized Nonvanishing Conjecture holds for threefolds with either $κ>0$ or $q>0$. As a result, we can prove the Iitaka conjecture $C_{n,m}$ holds for $n=7$ if the source space has non-negative Kodaira dimension, if the general fibre has positive Kodaira dimension, or if the base space is not threefold with $κ=q=0$. In particular, $C^-_{n,m}$ holds if $n\leq 7$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_04015 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Generalized Nonvanishing Conjecture and Iitaka Conjecture Chang, Chi-Kang Algebraic Geometry In this article, we will prove the Generalized Nonvanishing Conjecture holds for threefolds with either $κ>0$ or $q>0$. As a result, we can prove the Iitaka conjecture $C_{n,m}$ holds for $n=7$ if the source space has non-negative Kodaira dimension, if the general fibre has positive Kodaira dimension, or if the base space is not threefold with $κ=q=0$. In particular, $C^-_{n,m}$ holds if $n\leq 7$. |
| title | Generalized Nonvanishing Conjecture and Iitaka Conjecture |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2312.04015 |