Campana rational connectedness and weak approximation
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
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| _version_ | 1866915253571289088 |
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| author | Chen, Qile Lehmann, Brian Tanimoto, Sho |
| author_facet | Chen, Qile Lehmann, Brian Tanimoto, Sho |
| contents | Campana introduced a notion of Campana rational connectedness for Campana orbifolds. Given a Campana fibration over a complex curve, we prove that a version of weak approximation for Campana sections holds at places of good reduction when the general fiber satisfies a slightly stronger version of Campana rational connectedness. Campana also conjectured that any Fano orbifold is Campana rationally connected; we verify a stronger statement for toric Campana orbifolds. A key tool in our study is log geometry and moduli stacks of stable log maps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_04991 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Campana rational connectedness and weak approximation Chen, Qile Lehmann, Brian Tanimoto, Sho Algebraic Geometry Campana introduced a notion of Campana rational connectedness for Campana orbifolds. Given a Campana fibration over a complex curve, we prove that a version of weak approximation for Campana sections holds at places of good reduction when the general fiber satisfies a slightly stronger version of Campana rational connectedness. Campana also conjectured that any Fano orbifold is Campana rationally connected; we verify a stronger statement for toric Campana orbifolds. A key tool in our study is log geometry and moduli stacks of stable log maps. |
| title | Campana rational connectedness and weak approximation |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2406.04991 |