Algebraic cycles and Fano threefolds of genus 10

Abstract

We show that prime Fano threefolds $Y$ of genus 10 have a multiplicative Chow-Künneth decomposition, in the sense of Shen-Vial. As a consequence, a certain tautological subring of the Chow ring of powers of $Y$ injects into cohomology.

arXiv comment24 pages, to appear in Bulletin de la SMF, comments welcome ! arXiv admin note: text overlap with arXiv:2110.11791, arXiv:2301.01961, arXiv:2105.02016