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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.07591 |
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| _version_ | 1866915500024397824 |
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| author | Pollock, Andrew Ito, Atsushi Szendroi, Balazs |
| author_facet | Pollock, Andrew Ito, Atsushi Szendroi, Balazs |
| contents | We introduce a cohomological method to compute Cox rings of hypersurfaces in the ambient space P^1 x P^n, which is more direct than existing methods. We prove that smooth hypersurfaces defined by regular sequences of coefficients are Mori dream spaces, generalizing a result of Ottem. We also compute Cox rings of certain specialized examples. In particular, we compute Cox rings in the well-studied family of Calabi--Yau threefolds of bidegree (2,4) in P^1 x P^3, determining explicitly how the Cox ring can jump discontinuously in a smooth family. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_07591 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Cox rings of some hypersurfaces Pollock, Andrew Ito, Atsushi Szendroi, Balazs Algebraic Geometry We introduce a cohomological method to compute Cox rings of hypersurfaces in the ambient space P^1 x P^n, which is more direct than existing methods. We prove that smooth hypersurfaces defined by regular sequences of coefficients are Mori dream spaces, generalizing a result of Ottem. We also compute Cox rings of certain specialized examples. In particular, we compute Cox rings in the well-studied family of Calabi--Yau threefolds of bidegree (2,4) in P^1 x P^3, determining explicitly how the Cox ring can jump discontinuously in a smooth family. |
| title | On the Cox rings of some hypersurfaces |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2504.07591 |