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arXiv · 2504.17475

Odd fake $\mathbb{Q}$ -homology quadrics exist

Fabrizio Catanese
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Abstract

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.

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Fabrizio Catanese. 2025-04-24. Odd fake $\mathbb{Q}$ -homology quadrics exist. https://arxiv.org/abs/2504.17475

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