Otwinowska, Anna. (2002) Composantes de dimension maximale d'un analogue du lieu de Noether-Lefschetz. Compositio Mathematica, Vol.13 (No.1). pp. 31-50. ISSN 0010-437X

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Abstract

Let X [subset or is implied by] $\mathbb P$4$\mathbb _C$ be a smooth hypersurface of degree d [gt-or-equal, slanted] 5, and let S [subset or is implied by] X be a smooth hyperplane section. Assume that there exists a non trivial cycle Z [set membership] Pic(X) of degree 0, whose image in CH1(X) is in the kernel of the Abel–Jacobi map. The family of couples (X, S) containing such Z is a countable union of analytic varieties. We show that it has a unique component of maximal dimension, which is exaclty the locus of couples (X, S) satisfying the following condition: There exists a line Δ [subset or is implied by] S and a plane P [subset or is implied by] $\mathbb P$4$_{\mathbb C}$ such that P [cap B: intersection] X = Δ, and Z = Δ − dh, where h is the class of the hyperplane section in CH1(S). The image of Z in CH1(X) is thus 0. This construction provides evidence for a conjecture by Nori which predicts that the Abel–Jacobi map for 1–cycles on X is injective.

Item Type:	Journal Article
Alternative Title:	Components of Maximal Dimension of an Analogue of the Noether-Lefschetz Locus
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH):	Algebraic cycles, Hodge theory, Geometry, Algebraic, Hypersurfaces, Geometry, Projective
Journal or Publication Title:	Compositio Mathematica
Publisher:	Cambridge University Press
ISSN:	0010-437X
Date:	March 2002
Volume:	Vol.13
Number:	No.1
Page Range:	pp. 31-50
Identification Number:	10.1023/A:1014751331345
Status:	Peer Reviewed
Access rights to Published version:	Open Access
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URI:	http://wrap.warwick.ac.uk/id/eprint/787

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