# Algebraic cycles and intersections of three quadrics

@article{Laterveer2021AlgebraicCA, title={Algebraic cycles and intersections of three quadrics}, author={Robert Laterveer}, journal={Mathematical Proceedings of the Cambridge Philosophical Society}, year={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 consequence, the Chow ring of (powers of) Y displays K3-like behaviour. As a by-product of the argument, we also establish a multiplicative Chow–Künneth decomposition for double planes.

## One Citation

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…

## References

SHOWING 1-10 OF 61 REFERENCES

Finite-dimensionality and cycles on powers of K3 surfaces

- Mathematics
- 2014

For a K3 surface S, consider the subring of CH(S^n) generated by divisor and diagonal classes (with Q-coefficients). Voisin conjectures that the restriction of the cycle class map to this ring is…

Algebraic cycles and Fano threefolds of genus 8

- Mathematics
- 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…

On a conjectural filtration on the Chow groups of an algebraic variety

- Mathematics
- 1993

Abstract In this paper we describe a conjectural filtration on the Chow groups of a projective, smooth variety. This filtration is suggested by, and based upon, Grothendieck's theory of motives…

Algebraic cycles and Verra fourfolds

- Mathematics
- 2019

This note is about the Chow ring of Verra fourfolds. For a general Verra fourfold, we show that the Chow group of homologically trivial $1$-cycles is generated by conics. We also show that Verra…

The Chow Ring of a Cubic Hypersurface

- Mathematics
- 2019

We study the product structure on the Chow ring (with rational coefficients) of a cubic hypersurface in projective space and prove that the image of the product map is as small as possible.

An interesting 0-cycle

- Mathematics
- 2003

The geometric and arithmetic properties of a smooth algebraic variety X are reflected by the configuration of its subvarieties. A principal invariant of these are the Chow groupsCHp(X), defined to be…

THE CHOW RINGS

- Mathematics
- 1996

The properties of a toric variety have strong connection with the combinatorial structure of the corresponding fan and the rela- tions among the generators. Using this fact, we have described explic-…

Decomposable cycles and Noether-Lefschetz loci

- Mathematics
- 2015

We prove that there exist smooth surfaces of degree d in projective 3-space such that the group of rational equivalence classes of decomposable 0-cycles has rank at least the integer part of (d-1)/3.

ON THE CHOW RING OF A K3 SURFACE

- Mathematics
- 2001

We show that the Chow group of 0-cycles on a K3 surface contains a class of degree 1 with remarkable properties: any product of divisors is proportional to this class, and so is the second Chern…

The Fourier Transform for Certain Hyperkahler Fourfolds

- Mathematics
- 2013

Using a codimension-1 algebraic cycle obtained from the Poincare line bundle, Beauville defined the Fourier transform on the Chow groups of an abelian variety A and showed that the Fourier transform…