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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.14850 |
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| _version_ | 1866914618797981696 |
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| author | Fay, Aideen |
| author_facet | Fay, Aideen |
| contents | We show that the very general Verra fourfold is irrational, using the Hodge atom framework of Katzarkov--Kontsevich--Pantev--Yu. Two novel points are: a refined analysis of Hodge atoms, based on the involution on the cohomology of $X$, and a derivation of the quantum multiplication matrix from the quantum differential operator. This gives the first successful application of the method of Hodge atoms to a space with Picard rank greater than one. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_14850 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Very General Verra Fourfold is Irrational Fay, Aideen Algebraic Geometry We show that the very general Verra fourfold is irrational, using the Hodge atom framework of Katzarkov--Kontsevich--Pantev--Yu. Two novel points are: a refined analysis of Hodge atoms, based on the involution on the cohomology of $X$, and a derivation of the quantum multiplication matrix from the quantum differential operator. This gives the first successful application of the method of Hodge atoms to a space with Picard rank greater than one. |
| title | The Very General Verra Fourfold is Irrational |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2604.14850 |