# Algebraic cycles and Fano threefolds of genus 8

@inproceedings{Laterveer2021AlgebraicCA, title={Algebraic cycles and Fano threefolds of genus 8}, author={Robert Laterveer}, year={2021} }

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.

## 5 Citations

Some new Fano varieties with a multiplicative Chow-K\"unneth decomposition

- Mathematics
- 2021

Let Y be a smooth dimensionally transverse intersection of the GrassmannianGr(2, n) with 3 Plücker hyperplanes. We show that Y admits a multiplicative Chow–Künneth decomposition, in the sense of…

Some Motivic Properties of Gushel-Mukai Sixfolds

- Mathematics
- 2022

Gushel-Mukai sixfolds are an important class of so-called FanoK3 varieties. In this paper we show that they admit a multiplicative ChowKünneth decomposition modulo algebraic equivalence and that they…

Algebraic cycles and intersections of three quadrics

- MathematicsMathematical Proceedings of the Cambridge Philosophical Society
- 2021

Let Y be a smooth complete intersection of three quadrics, and assume the dimension of Y is even. We show that Y has a multiplicative Chow–Künneth decomposition, in the sense of Shen–Vial. As a…

Algebraic cycles and intersections of a quadric and a cubic

- Mathematics
- 2021

Abstract Let Y be a smooth complete intersection of a quadric and a cubic in ℙn{\mathbb{P}^{n}}, with n even. We show that Y has a multiplicative Chow–Künneth decomposition, in the sense of…

Algebraic Cycles and Intersections of 2 Quadrics

- Mathematics
- 2021

A smooth intersection Y of two quadrics in P has Hodge level 1. We show that such varieties Y have a multiplicative Chow–Künneth decomposition, in the sense of Shen–Vial. As a consequence, a certain…

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