On the Chow ring of Fano fourfolds of K3 type

Michele Bolognesi (1) , Robert Laterveer (2)

1 IMAG - Institut Montpelliérain Alexander Grothendieck
2 IRMA - Institut de Recherche Mathématique Avancée

We show that a wide range of Fano varieties of K3 type, recently constructed by Bernardara, Fatighenti, Manivel and Tanturri in [6], 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.

Domaines: Géométrie algébrique [math.AG]

Michele Bolognesi, Robert Laterveer. On the Chow ring of Fano fourfolds of K3 type. 2022. ⟨hal-03824684⟩