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Composantes de dimension maximale d'un analogue du lieu de NoetherLefschetz
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Otwinowska, Anna (2002) Composantes de dimension maximale d'un analogue du lieu de NoetherLefschetz. Compositio Mathematica, Vol.13 (No.1). pp. 3150. doi:10.1023/A:1014751331345

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Official URL: http://dx.doi.org/10.1023/A:1014751331345
Abstract
Let X [subset or is implied by] $\mathbb P$4$\mathbb _C$ be a smooth hypersurface of degree d [gtorequal, 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 NoetherLefschetz 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:  0010437X  
Official Date:  March 2002  
Dates: 


Volume:  Vol.13  
Number:  No.1  
Page Range:  pp. 3150  
DOI:  10.1023/A:1014751331345  
Status:  Peer Reviewed  
Access rights to Published version:  Open Access 
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