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arXiv · 2608.12950

Algebraic cycles and Fano threefolds of genus 7

Robert Laterveer
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Abstract

Let $Y$ be a very general prime Fano threefold of genus 7. We exhibit an explicit 2-cycle on $Y\times Y$ that is Abel-Jacobi trivial but non-torsion in the Chow group $A^4(Y\times Y)$. As a consequence, $Y$ does not admit a multiplicative Chow-K\"unneth decomposition, in the sense of Shen-Vial. We also show that any Fano threefold has a multiplicative Chow-K\"unneth decomposition modulo algebraic equivalence.

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Robert Laterveer. 2026-08-13. Algebraic cycles and Fano threefolds of genus 7. https://arxiv.org/abs/2608.12950

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