On the Chow ring of Fano varieties on the Fatighenti-Mongardi list
Robert Laterveer

TL;DR
This paper proves that many Fano varieties of K3 type constructed by Fatighenti-Mongardi admit a multiplicative Chow-K"unneth decomposition, impacting the understanding of their Chow rings.
Contribution
It establishes the existence of a multiplicative Chow-K"unneth decomposition for numerous Fano varieties of K3 type from the Fatighenti-Mongardi list, confirming a conjecture.
Findings
Many Fano varieties of K3 type admit a multiplicative Chow-K"unneth decomposition.
This result has significant implications for the structure of their Chow rings.
The work confirms a conjecture for a broad class of Fano varieties.
Abstract
Conjecturally, Fano varieties of K3 type admit a multiplicative Chow-K\"unneth decomposition, in the sense of Shen-Vial. We prove this for many of the families of Fano varieties of K3 type constructed by Fatighenti-Mongardi. This has interesting consequences for the Chow ring of these varieties.
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