Odd and even fake quadrics isogenous to a product

Fabrizio Catanese; JongHae Keum; Do Geun Kim; Kyoung-Seog Lee

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arXiv · 2611.06077

Odd and even fake quadrics isogenous to a product

Fabrizio Catanese·JongHae Keum·Do Geun Kim·Kyoung-Seog Lee

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Abstract

A $\mathbb{Q}$-homology quadric is a smooth compact complex surface which has the same $\mathbb{Q}$-homology as a quadric surface, that is, the product of two $2$-dimensional spheres. It is called fake if it is minimal and not rational. Among them are the fake quadrics which are isogenous to a product of complex curves. In this paper, we determine the parity of the intersection forms of all fake quadrics isogenous to a product of unmixed type. In particular, we show that there are fake quadrics with odd intersection forms.

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BibTeX RIS

Fabrizio Catanese, JongHae Keum, Do Geun Kim, Kyoung-Seog Lee. 2026-11-04. Odd and even fake quadrics isogenous to a product. https://arxiv.org/abs/2611.06077

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