# ON THE CHOW RING OF A K3 SURFACE

@article{Beauville2001ONTC, title={ON THE CHOW RING OF A K3 SURFACE}, author={Arnaud Beauville}, journal={Journal of Algebraic Geometry}, year={2001}, volume={13}, pages={417-426} }

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 class c2.

## 157 Citations

Chow groups and derived categories of K3 surfaces

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- 2009

This survey is based on my talk at the conference `Classical algebraic geometry today' at the MSRI. Some new results on the action of symplectomorphisms on the Chow group are added.

The Chow Ring of a Cubic Hypersurface

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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.

Algebraic cycles and Fano threefolds of genus 8

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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…

Algebraic Cycles and Intersections of 2 Quadrics

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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…

On the Chow ring of certain Fano fourfolds

- Mathematics
- 2020

We prove that certain Fano fourfolds of K3 type constructed by Fatighenti–Mongardi have a multiplicative Chow–Kunneth decomposition. We present some consequences for the Chow ring of these fourfolds.

Stable Vector Bundles as Generators of the Chow Ring

- Mathematics
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In this paper we show that the family of stable vector bundles gives a set of generators for the Chow ring, the K-theory and the derived category of any smooth projective variety.

The Chow ring of double EPW sextics

- Mathematics
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A conjecture of Beauville and Voisin states that for an irreducible symplectic variety X, any polynomial relation between classes of divisors and the Chern classes of X which holds in cohomology…

On the motive of some hyperKaehler varieties

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We show that the motive of the Hilbert scheme of length-$n$ subschemes on a K3 surface or on an abelian surface admits a decomposition similar to the decomposition of the motive of an abelian variety…

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- Mathematics
- 2018

We propose a "Bloch type" conjecture for surfaces: if the cup product map in coherent cohomology is zero, then all intersections of homologically trivial divisors should be zero in the Chow group of…

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

- Mathematics
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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…

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