Roitman's theorem for singular complex projective surfaces

Details Roitman's theorem for singular complex projective surfaces Roitman's theorem for singular complex projective surfaces

1995-03-29

arxiv.org/abs/alg-geom/9503022v1

Duke Math. J. 84 (1996), 155-190

Mathematics

Algebraic Geometry

36 pages, LaTeX

Scientific paper

Let $X$ be a complex projective surface with arbitrary singularities. We construct a generalized Abel--Jacobi map $A_0(X)\to J^2(X)$ and show that it is an isomorphism on torsion subgroups. Here $A_0(X)$ is the appropriate Chow group of smooth 0-cycles of degree 0 on $X$, and $J^2(X)$ is the intermediate Jacobian associated with the mixed Hodge structure on $H^3(X)$. Our result generalizes a theorem of Roitman for smooth surfaces: if $X$ is smooth then the torsion in the usual Chow group $A_0(X)$ is isomorphic to the torsion in the usual Albanese variety $J^2(X)\cong Alb(X)$ by the classical Abel-Jacobi map.

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