author={Arnaud Beauville},
  journal={Journal of Algebraic Geometry},
  • A. Beauville
  • Published 10 September 2001
  • Mathematics
  • Journal of Algebraic Geometry
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. 
Chow groups and derived categories of K3 surfaces
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
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
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
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
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
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
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
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
A remark on the Chow ring of Sicilian surfaces
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
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


The Torsion of the Group of 0-Cycles Modulo Rational Equivalence
In this work we continue the study of rational equivalence of O-cycles on nonsingular projective varieties over an algebraically closed field k, which we began in [13], [14]. The main result of this
Some elementary theorems about algebraic cycles on abelian varieties
The structure of the group of 0-cycles modulo rational equivalence on ann-dimensional abelian varietyA over an algebraically closed fieldk is studied. This group forms an augmented ℤ-algebra under
Rational equivalence of 0-cycles on surfaces
We will consider in this note 0-cycles on a complete non-singular algebraic surface F over the field C o f complex numbers. We will use the language o f schemes, and every scheme will be assumed
The modified diagonal cycle on the triple product of a pointed curve
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On the Picard number of a Fermat surface
Mumford's theorem on curves on K3 surfaces. Algebraic Geometry
  • LN 1016
  • 1982
Rational equivalence of 0cycles on surfaces
  • J . Math . Kyoto Univ .
  • 1968