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### Components of maximal dimension of an analogue of the Noether-Lefschetz locus

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UNSPECIFIED.
(2002)
*Components of maximal dimension of an analogue of the Noether-Lefschetz locus.*
COMPOSITIO MATHEMATICA, 131
(1).
pp. 31-50.
ISSN 0010-437X

**Full text not available from this repository.**

## Abstract

Let x subset of P-C(4) be a smooth hypersurface of degree d greater than or equal to 5, and let S subset of X be a smooth hyperplane section. assume that there exists a non trivial cycle Z is an element of 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 Delta subset of S and a plane P subset of P-C(4) such that P boolean AND X = Delta, and z = Delta - 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 |
---|---|

Subjects: | Q Science > QA Mathematics |

Journal or Publication Title: | COMPOSITIO MATHEMATICA |

Publisher: | KLUWER ACADEMIC PUBL |

ISSN: | 0010-437X |

Official Date: | March 2002 |

Volume: | 131 |

Number: | 1 |

Number of Pages: | 20 |

Page Range: | pp. 31-50 |

Publication Status: | Published |

URI: | http://wrap.warwick.ac.uk/id/eprint/11155 |

Data sourced from Thomson Reuters' Web of Knowledge

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