Quantum cohomology and irrationality of Gushel-Mukai fourfolds
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866918525644308480 |
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| author | Benedetti, Vladimiro Manivel, Laurent Perrin, Nicolas |
| author_facet | Benedetti, Vladimiro Manivel, Laurent Perrin, Nicolas |
| contents | We compute the small quantum cohomology of Gushel-Mukai fourfolds. Following [13], our computations imply that the very general ones are not rational. Following [8], and thanks to a suitable deformation of the small quantum cohomology ring, we also deduce that a rational Gushel-Mukai fourfold has the same rational cohomology as some K3 surface. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_17487 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quantum cohomology and irrationality of Gushel-Mukai fourfolds Benedetti, Vladimiro Manivel, Laurent Perrin, Nicolas Algebraic Geometry We compute the small quantum cohomology of Gushel-Mukai fourfolds. Following [13], our computations imply that the very general ones are not rational. Following [8], and thanks to a suitable deformation of the small quantum cohomology ring, we also deduce that a rational Gushel-Mukai fourfold has the same rational cohomology as some K3 surface. |
| title | Quantum cohomology and irrationality of Gushel-Mukai fourfolds |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2603.17487 |