Complete intersections with middle Picard number 1 defined over \({\mathbb{Q}}\)
type: Item
instance of: scholarly article
title: Complete intersections with middle Picard number 1 defined over \({\mathbb{Q}}\)
zbMATH Open document ID: 0579.14006
DOI: 10.1007/BF01175050
author: Tomohide Terasoma
published in: Mathematische Zeitschrift
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173582
review text: Let X be a non-singular complete intersection in a projective space over the complex number field. It is known that the cohomology \(H^{2i}(X,{\mathbb{Q}})\) is generated by the powers of the class of the hyperplane section except for the case \(2i=\dim X\). In this case, the dimension of the space of algebraic cycles of codimension i viewed as a \({\mathbb{Q}}\)-subvectorspace of \(H^{2i}(X,{\mathbb{Q}})\) is called the middle Picard number of X. \textit{P. Deligne} [SGA 7 II, Lect. Notes Math. 340 (1973] showed that X has the middle Picard number 1 if X has a type different from (2;3), (2n;2), (2n;2,2). Here a complete intersection is said to be of type (N;\b{a}), where \b{a}\(=a_ 1,...,a_ d\) is a sequence of positive integers, if it is a complete intersection of hypersurfaces of degree \(a_ 1,...,a_ d\) in \(P^{N+d}\). The paper under review proves that for a type as above, there exists a complete intersection of middle Picard number 1.
Mathematics Subject Classification ID: 14C22
Mathematics Subject Classification ID: 14M10
zbMATH DE Number: 3927068
zbMATH Keywords: algebraic cycle
zbMATH Keywords: type of a complete intersection
zbMATH Keywords: middle Picard number
reviewed by: Trung Ngo Viet
MaRDI profile type: Publication
cites work: La conjecture de Weil. II
cites work: Q5724382
cites work: Q3871006
cites work: Q5580319
OpenAlex ID: W2092079204
description: scientific article; zbMATH DE number 3927068