Roitman’s theorem for singular complex projective surfaces
نویسندگان
چکیده
Let X be a complex projective surface with arbitrary singularities. We construct a generalized Abel–Jacobi map A0(X) → J 2(X) and show that it is an isomorphism on torsion subgroups. Here A0(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 A0(X) is isomorphic to the torsion in the usual Albanese variety J2(X) ∼= Alb(X) by the classical Abel-Jacobi map. ∗ Members of GNSAGA of CNR, partially supported by ECC Science Plan ∗∗ Partially supported by NSF grants
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