The Chow ring of a K3 surface

2001/11/13 by Arnaud Beauville, Claire Voisin, Beauville, Arnaud +1 · 2 citations
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.math/0111146

10 pages, Plain TeX. Supersedes AG/0109063

arxiv created 2001/11/13 · arxiv updated 2009/11/30

Abstract

Let X be a K3 surface. We show that the Chow group CH₀(X) of 0-cycles contains a "fundamental class" c_X of degree 1 with remarkable properties: any product of divisors is proportional to this class, and so is the second Chern class c₂(X). This preprint supersedes the preprint math.AG/0109063 by the first author, where the latter property was conjectured.

Cited by

• Motivic multiplicativity of complete intersections
• Strong BSD for abelian surfaces and the Bloch-Beilinson conjecture

Related

• On the Chow ring of a K3 surface
• The Chow group of zero-cycles on certain Châtelet surfaces over local fields
• Rational equivalence of 0-cycles on K3 surfaces and conjectures of Huybrechts and O'Grady
• On 0-cycles with modulus
• Moduli of sheaves and the Chow group of K3 surfaces