Algebraic cycles and Fano threefolds of genus 8
Robert Laterveer

TL;DR
This paper proves that prime Fano threefolds of genus 8 possess a special Chow-K"unneth decomposition, leading to injectivity results for certain subrings of their Chow rings into cohomology.
Contribution
It establishes the existence of a multiplicative Chow-K"unneth decomposition for prime Fano threefolds of genus 8, a new structural property in algebraic geometry.
Findings
Prime Fano threefolds of genus 8 have a multiplicative Chow-K"unneth decomposition.
A tautological subring of the Chow ring injects into cohomology.
The result advances understanding of the Chow ring structure of Fano threefolds.
Abstract
We show that prime Fano threefolds of genus 8 have a multiplicative Chow-K\"unneth decomposition, in the sense of Shen-Vial. As a consequence, a certain tautological subring of the Chow ring of powers of injects into cohomology.
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