On canonical bundle formula for fibrations of curves with arithmetic genus one
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866914452241121280 |
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| author | Chen, Jingshan Wang, Chongning Zhang, Lei |
| author_facet | Chen, Jingshan Wang, Chongning Zhang, Lei |
| contents | In this paper, we develop canonical bundle formulas for fibrations of relative dimension one in characteristic $p>0$. For such a fibration from a log pair $f\colon (X, Δ) \to S$, if $f$ is separable, we can obtain a formula similar to the one due to Witaszek \cite{Wit21}; if $f$ is inseparable, we treat the case when $S$ is of maximal Albanese dimension. As an application, we prove that for a klt pair $(X,Δ)$ with $-(K_X+Δ)$ nef, if the Albanese morphism $a_X\colon X \to A$ is of relative dimension one, then $X$ is a fiber space over $A$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_08927 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On canonical bundle formula for fibrations of curves with arithmetic genus one Chen, Jingshan Wang, Chongning Zhang, Lei Algebraic Geometry 14G17, 14D06 In this paper, we develop canonical bundle formulas for fibrations of relative dimension one in characteristic $p>0$. For such a fibration from a log pair $f\colon (X, Δ) \to S$, if $f$ is separable, we can obtain a formula similar to the one due to Witaszek \cite{Wit21}; if $f$ is inseparable, we treat the case when $S$ is of maximal Albanese dimension. As an application, we prove that for a klt pair $(X,Δ)$ with $-(K_X+Δ)$ nef, if the Albanese morphism $a_X\colon X \to A$ is of relative dimension one, then $X$ is a fiber space over $A$. |
| title | On canonical bundle formula for fibrations of curves with arithmetic genus one |
| topic | Algebraic Geometry 14G17, 14D06 |
| url | https://arxiv.org/abs/2308.08927 |