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Composantes de dimension maximale d'un analogue du lieu de Noether-Lefschetz
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Otwinowska, Anna (2002) Composantes de dimension maximale d'un analogue du lieu de Noether-Lefschetz. Compositio Mathematica, Vol.13 (No.1). pp. 31-50. doi:10.1023/A:1014751331345 ISSN 0010-437X.
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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 [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 | ||||
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Alternative Title: | Components of Maximal Dimension of an Analogue of the Noether-Lefschetz Locus | ||||
Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > 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 | ||||
Official Date: | March 2002 | ||||
Dates: |
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Volume: | Vol.13 | ||||
Number: | No.1 | ||||
Page Range: | pp. 31-50 | ||||
DOI: | 10.1023/A:1014751331345 | ||||
Status: | Peer Reviewed | ||||
Access rights to Published version: | Open Access (Creative Commons) |
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