The quartic threefold is symplectically irrational
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918528834076672 |
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| author | Cai, Jiaji |
| author_facet | Cai, Jiaji |
| contents | We prove that smooth quartic threefolds are symplectically irrational, i.e., cannot be related to projective space by a series of symplectic blow-ups, blow-downs, and deformations. This implies that they are algebraically irrational, recovering a classical result of Iskovskikh-Manin. Our proof involves establishing a decomposition theorem for quantum cohomology along symplectic blow-ups, following the work of Iritani. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_29143 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The quartic threefold is symplectically irrational Cai, Jiaji Symplectic Geometry Algebraic Geometry 53D35 (Primary), 53D45 (Secondary) We prove that smooth quartic threefolds are symplectically irrational, i.e., cannot be related to projective space by a series of symplectic blow-ups, blow-downs, and deformations. This implies that they are algebraically irrational, recovering a classical result of Iskovskikh-Manin. Our proof involves establishing a decomposition theorem for quantum cohomology along symplectic blow-ups, following the work of Iritani. |
| title | The quartic threefold is symplectically irrational |
| topic | Symplectic Geometry Algebraic Geometry 53D35 (Primary), 53D45 (Secondary) |
| url | https://arxiv.org/abs/2605.29143 |