Quantum cohomology and birational geometry of Verra fourfolds
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917545026519040 |
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| author | Benedetti, Vladimiro Guéré, Jérémy Manivel, Laurent Perrin, Nicolas |
| author_facet | Benedetti, Vladimiro Guéré, Jérémy Manivel, Laurent Perrin, Nicolas |
| contents | We compute the small quantum cohomology ring of a Verra fourfold. Using the theory of atoms recently developped by Katzarkov--Kontsevich--Pantev--Yu, and building on recent papers of the authors, we deduce that a Verra fourfold is never birational to a very general cubic fourfold, nor to a very general Gushel--Mukai fourfold, whereas it was previously known that a general Verra fourfold is birational to a general nodal Gushel--Mukai fourfold. More precisely, we show that for every smooth cubic fourfold or smooth Gushel--Mukai fourfold that is birational to some Verra fourfold, the primitive cohomology is isomorphic, as a rational Hodge structure, to the middle cohomology of some projective K3 surface. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_30450 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quantum cohomology and birational geometry of Verra fourfolds Benedetti, Vladimiro Guéré, Jérémy Manivel, Laurent Perrin, Nicolas Algebraic Geometry 14E08, 14N35 We compute the small quantum cohomology ring of a Verra fourfold. Using the theory of atoms recently developped by Katzarkov--Kontsevich--Pantev--Yu, and building on recent papers of the authors, we deduce that a Verra fourfold is never birational to a very general cubic fourfold, nor to a very general Gushel--Mukai fourfold, whereas it was previously known that a general Verra fourfold is birational to a general nodal Gushel--Mukai fourfold. More precisely, we show that for every smooth cubic fourfold or smooth Gushel--Mukai fourfold that is birational to some Verra fourfold, the primitive cohomology is isomorphic, as a rational Hodge structure, to the middle cohomology of some projective K3 surface. |
| title | Quantum cohomology and birational geometry of Verra fourfolds |
| topic | Algebraic Geometry 14E08, 14N35 |
| url | https://arxiv.org/abs/2605.30450 |