A variant of a theorem of C. Voisin
type: Item
instance of: scholarly article
title: A variant of a theorem of C. Voisin
zbMATH Open document ID: 1002.14001
DOI: 10.1016/S0019-3577(01)80028-8
published in: Indagationes Mathematicae. New Series
publication date: 2002-06-23T00:00:00Z
review text: 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.
reviewed by: Lucian Bădescu
Mathematics Subject Classification ID: 14C15
Mathematics Subject Classification ID: 14J25
Mathematics Subject Classification ID: 14C25
Mathematics Subject Classification ID: 14H50
zbMATH DE Number: 1758187
zbMATH Keywords: complex surfaces
zbMATH Keywords: zero cycles
zbMATH Keywords: curve on a surface
author: J. Nagel
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1758187