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

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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
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

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