Algebraic cycles and Fano threefolds of genus 8

Abstract

We show that prime Fano threefolds $Y$ of genus 8 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.

20 pages, to appear in Portugaliae Mathematica, comments welcome ! arXiv admin note: text overlap with arXiv:2105.02016, arXiv:2105.02224, arXiv:2009.11061, arXiv:2108.08547