On the Iitaka conjecture for anticanonical divisors in positive characteristic
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866917362545983488 |
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| author | Benozzo, Marta |
| author_facet | Benozzo, Marta |
| contents | Given a fibration over a perfect field of positive characteristic, we study an Iitaka-type inequality for the anticanonical divisors. We conclude that it holds when the source of the fibration is a threefold or when the target is a curve, the general fibre is regular and the pair induced on it from the ambient space is strongly F-regular. We then give counterexamples in characteristics 2 and 3 for fibrations with non-normal fibres, constructed from Tango--Raynaud surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_02045 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On the Iitaka conjecture for anticanonical divisors in positive characteristic Benozzo, Marta Algebraic Geometry 14D06, 14G17 Given a fibration over a perfect field of positive characteristic, we study an Iitaka-type inequality for the anticanonical divisors. We conclude that it holds when the source of the fibration is a threefold or when the target is a curve, the general fibre is regular and the pair induced on it from the ambient space is strongly F-regular. We then give counterexamples in characteristics 2 and 3 for fibrations with non-normal fibres, constructed from Tango--Raynaud surfaces. |
| title | On the Iitaka conjecture for anticanonical divisors in positive characteristic |
| topic | Algebraic Geometry 14D06, 14G17 |
| url | https://arxiv.org/abs/2204.02045 |