Roitman's theorem for singular complex projective surfaces, by Luca Barbieri-Viale, Claudio Pedrini, and Charles Weibel

Let X be a complex projective surface, not necessarily smooth. We construct and study a natural map from the Chow group of smooth zero-cycles on X to Griffith's Intermediate Jacobian. Our main result is that this is an isomorphism modulo torsion.

The Intermediate Jacobian is an extension of an abelian variety by a torus (a 1-motive), so its torsion subgroup is easily determined. If X is smooth, our map is the classical Abel-Jacobi map and our main result reduces to Roitman's Theorem. If X is normal, our result follows from work of Collino and Levine. Our main tool is the Chern class from K-theory to Deligne-Beilinson cohomology.

This has appeared in Duke J. Math., 84 (1996), 155-190.

Luca Barbieri-Viale <>
Claudio Pedrini <>
Charles Weibel <>