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We show that a wide range of Fano varieties of K3 type, recently constructed by Bernardara, Fatighenti, Manivel and Tanturri in (Fano fourfolds of K3 type, arXiv:2111.13030), have a multiplicative Chow–Künneth decomposition, in the sense of Shen–Vial. It follows that the Chow ring of these Fano varieties behaves like that of K3 surfaces. As a side result, we obtain some criteria for the Franchetta property of blown-up projective varieties.

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On the Chow Ring of Fano Fourfolds of K3 Type

  • 章节

  • 发表日期：

    2025年

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  • Michele Bolognesi,
  • Robert Laterveer

摘要

We show that a wide range of Fano varieties of K3 type, recently constructed by Bernardara, Fatighenti, Manivel and Tanturri in (Fano fourfolds of K3 type, arXiv:2111.13030), have a multiplicative Chow–Künneth decomposition, in the sense of Shen–Vial. It follows that the Chow ring of these Fano varieties behaves like that of K3 surfaces. As a side result, we obtain some criteria for the Franchetta property of blown-up projective varieties.