On the Chow Ring of Fano Fourfolds of K3 type

Abstract

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

arXiv comment19 pages, comments welcome. Version 2: revised according to referee's comments. To appear in "Perspectives on four decades: Algebraic geometry 1980---2020. In memory of Alberto Collino'', Trends in Mathematics, Birkhaüser,