Odd fake $\mathbb{Q}$ -homology quadrics exist
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911118272757760 |
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| author | Catanese, Fabrizio |
| author_facet | Catanese, Fabrizio |
| contents | We show the existence of odd fake $\mathbb{Q}$-homology quadrics, namely of minimal surfaces $S$ of general type which have the same $\mathbb{Q}$-homology as a smooth quadric $Q \cong (\mathbb{P}^1(\mathbb{C}))^2$, but have an odd intersection form on $ H^2(S, \mathbb{Z})/Tors(S)$, where $Tors(S)$ is the Torsion subgroup.
Our examples are provided by a special 1-dimensional family of surfaces isogenous to a product of unmixed type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_17475 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Odd fake $\mathbb{Q}$ -homology quadrics exist Catanese, Fabrizio Algebraic Geometry Algebraic Topology 14J15, 14J25, 14J29, 14J80 We show the existence of odd fake $\mathbb{Q}$-homology quadrics, namely of minimal surfaces $S$ of general type which have the same $\mathbb{Q}$-homology as a smooth quadric $Q \cong (\mathbb{P}^1(\mathbb{C}))^2$, but have an odd intersection form on $ H^2(S, \mathbb{Z})/Tors(S)$, where $Tors(S)$ is the Torsion subgroup. Our examples are provided by a special 1-dimensional family of surfaces isogenous to a product of unmixed type. |
| title | Odd fake $\mathbb{Q}$ -homology quadrics exist |
| topic | Algebraic Geometry Algebraic Topology 14J15, 14J25, 14J29, 14J80 |
| url | https://arxiv.org/abs/2504.17475 |