A variant of a theorem of C. Voisin
Let \(C\) be a smooth curve on a smooth surface \(S\) of degree \(d\) in \(\mathbb P^3_{\mathbb C}\), and let \(i:C\hookrightarrow S\) be the inclusion morphism. Let \(i_*:A_0(C)\to A_0(S)\) be the induced map on the groups of \(0\)-cycles of degree zero modulo rational equivalence. Voisin studied the kernel of the map \(i_*\) by showing that \(\text{Tors}(A_0(C))= \text{Ker}(i_*)\) if \(S\) is a very general surface of degree \(d\geq 5\) and \(C\) is a smooth plane section of \(S\) [see \textit{C. Voisin}, Math. Ann. 299, No. 1, 77-103 (1994; Zbl 0837.14007)]. The main aim of the paper under review is to extend Vorsin's result to the case when the curve \(C\) is the intersection of \(S\) with a smooth hypersurface of arbitrary degree.
scientific article; zbMATH DE number 1758187
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