Abundance for threefolds in positive characteristic when $ν=2$
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866915940842602496 |
|---|---|
| author | Xu, Zheng |
| author_facet | Xu, Zheng |
| contents | In this paper, we prove the abundance conjecture for threefolds over a perfect field $k$ of characteristic $p > 3$ in the case of numerical dimension equals to $2$. More precisely, we prove that if $(X,B)$ be a projective lc threefold pair over $k$ such that $K_{X}+B$ is nef and $ν(K_{X}+B)=2$, then $K_{X}+B$ is semiample. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_03938 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Abundance for threefolds in positive characteristic when $ν=2$ Xu, Zheng Algebraic Geometry In this paper, we prove the abundance conjecture for threefolds over a perfect field $k$ of characteristic $p > 3$ in the case of numerical dimension equals to $2$. More precisely, we prove that if $(X,B)$ be a projective lc threefold pair over $k$ such that $K_{X}+B$ is nef and $ν(K_{X}+B)=2$, then $K_{X}+B$ is semiample. |
| title | Abundance for threefolds in positive characteristic when $ν=2$ |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2307.03938 |