The Picard number of certain algebraic surfaces
type: Item
instance of: scholarly article
title: The Picard number of certain algebraic surfaces
zbMATH Open document ID: 0788.14028
DOI: 10.1016/0022-4049(93)90145-J
author: B. J. J. Moonen
published in: Journal of Pure and Applied Algebra
publication date: 1993-05-16T00:00:00Z
review text: Consider the Picard number \(r\) of a nonsingular projective variety \(X\) (i.e., the rank of its Néron-Severi group) and its Lefschetz number (i.e. \(b_ 2-r\)). The author starts by reviewing some results Shioda which can be applied to compute the Picard number of a Fermat hypersurface and the Lefschetz number of a Delsarte surface. Afterwards families \(f:X\to S\) of algebraic varieties are considered; the theory of variation of Hodge structure is used to obtain an upper bound for the Picard number of the fibre \(X_ s\) of \(f\). The computation is made very explicit and effective for some families of algebraic surfaces (among which a family where one fibre is the Fermat surface of degree 5).
Mathematics Subject Classification ID: 14J10
Mathematics Subject Classification ID: 14D07
Mathematics Subject Classification ID: 14C22
Mathematics Subject Classification ID: 14G25
zbMATH DE Number: 167303
zbMATH Keywords: Picard number
zbMATH Keywords: Lefschetz number
zbMATH Keywords: Fermat hypersurface
zbMATH Keywords: Delsarte surface
zbMATH Keywords: variation of Hodge structure
zbMATH Keywords: families of algebraic surfaces
reviewed by: Marino Palleschi
MaRDI profile type: Publication
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full work available at URL: 0022-4049(93)90145-j
OpenAlex ID: W2036223412
description: scientific article; zbMATH DE number 167303