Algebraic Geometry
Chow groups of surfaces with h2,0⩽1
Comptes Rendus. Mathématique, Volume 338 (2004) no. 1, pp. 55-58.

We will investigate the geometry of rational equivalence classes of points on a surface S. We will show that if S is a general projective K3 surface then these equivalence classes are dense in the complex topology. We will also show that if S has the property that these equivalence classes are Zariski dense, then h2,0(S)⩽1.

Nous considérons la géométrie des classes d'équivalence rationelle des points d'une surface S. Nous montrons que si S est une surface K3 générale, ces classes d'équivalence sont denses pour la topologie complexe. Nous montrons également que si S a la propriété que ces classes d'équivalence sont Zariski dense, alors h2,0(S)⩽1.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2003.10.039
Maclean, Catriona 1

1 Institut de mathématiques de Jussieu, Université Paris 6, 175, rue de Chevaleret, 75013 Paris, France
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Maclean, Catriona. Chow groups of surfaces with h2,0⩽1. Comptes Rendus. Mathématique, Volume 338 (2004) no. 1, pp. 55-58. doi : 10.1016/j.crma.2003.10.039. http://www.numdam.org/articles/10.1016/j.crma.2003.10.039/

[1] Bloch, S. K2 of Artinian Q-algebras, with application to algebraic cycles, Comm. Algebra, Volume 3 (1975), pp. 405-428

[2] Bloch, S.; Kas, A.; Lieberman, D. Zero cycles on surfaces with pg=0, Compositio Math., Volume 33 (1976) no. 2, pp. 135-145

[3] Chen, X. Rational curves on K3 surfaces, J. Algebraic Geometry, Volume 8 (1999) no. 2, pp. 245-278

[4] Griffiths, P.; Green, M. Two applications of algebraic geometry to entire holomorphic mappings, The Chern Symposium 1979 (Proc. Internat. Sympos., Berkeley, CA, 1979), Springer, New York, 1980, pp. 41-74

[5] Mori, S.; Mukai, S. The uniruledness of the moduli space of curves of genus 11, Algebraic Geometry (Tokyo/Kyoto, 1982), Lecture Notes in Math., vol. 1016, Springer, Berlin, 1983, pp. 334-353

[6] Mumford, D. Rational equivalence of 0-cycles on surfaces, J. Math. Kyoto Univ., Volume 9 (1968), pp. 195-204

[7] Roitman, A. The torsion of the group of 0-cycles modulo rational equivalence, Ann. of Math. (2), Volume 111 (1980) no. 3, pp. 553-569

[8] Saint-Donat, B. Projective models of K3 surfaces, Amer. J. Math., Volume 96 (1974), pp. 602-639

[9] Voisin, C. Sur les zéro-cycles de certaines hypersurfaces munies d'un automorphisme, Ann. Scuola Norm. Sup. Pisa Cl. Sci., Volume 19 (1992) no. 4, pp. 473-492

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