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PreprintarXiv licencearXiv

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 ℚ-homology quadric is a smooth compact complex surface which has the same 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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Cite

BibTeXRIS
BibTeX
@misc{catanese2026even,
  title = {{Odd and even fake quadrics isogenous to a product}},
  author = {Fabrizio Catanese and JongHae Keum and Do Geun Kim and Kyoung-Seog Lee},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.06077},
  eprint = {2611.06077},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.06077},
}
RIS
TY  - UNPB
TI  - Odd and even fake quadrics isogenous to a product
AU  - Fabrizio Catanese
AU  - JongHae Keum
AU  - Do Geun Kim
AU  - Kyoung-Seog Lee
PY  - 2026
DA  - 2026/11/04
PB  - arXiv
DO  - 10.48550/arxiv.2611.06077
UR  - https://arxiv.org/abs/2611.06077
AB  - A ℚ-homology quadric is a smooth compact complex surface which has the same 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.
ER  -