On the Chow group and the intermediate Jacobian of a conic bundle
type: Item
instance of: scholarly article
title: On the Chow group and the intermediate Jacobian of a conic bundle
zbMATH Open document ID: 0589.14008
DOI: 10.1007/BF01763180
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 1985-01-01T00:00:00Z
review text: The author studies conic bundles X over a nonsingular surface S. Let \(A^ 2(X)\) denote the group of codimension 2 cycles which are algebraically equivalent to zero, and let J(X) be the intermediate Jacobian. The main result is that \(A^ 2(X)\) is naturally isogenous to \(A^ 2(S)\oplus A^ 1(S)\oplus P_ X\), where \(P_ X\) is the (generalized) Prym variety associated to X [this extends a result of \textit{A. Beauville}, Ann. Sci. Éc. Norm. Supér., IV. Sér. 10, 309-391 (1977; Zbl 0368.14018) where it is assumed that \(S={\mathbb{P}}^ 2]\). It is also shown that J(X) is isogenous to \(Alb(S)\oplus Pic^ 0(S)\oplus P_ X\).
reviewed by: F. L. Zak
Mathematics Subject Classification ID: 14C05
Mathematics Subject Classification ID: 14K30
zbMATH DE Number: 3946314
zbMATH Keywords: Chow group
zbMATH Keywords: conic bundles over a nonsingular surface
zbMATH Keywords: group of codimension 2 cycles
zbMATH Keywords: intermediate Jacobian
zbMATH Keywords: Prym variety
author: Mauro C. Beltrametti
MaRDI profile type: Publication
cites work: Variétés de Prym et jacobiennes intermédiaires
cites work: Prym varieties and Schottky problem
cites work: Q4103651
cites work: Q3277837
cites work: On the Schottky relation and its generalization to arbitrary genus
cites work: Q5609062
cites work: Q4195061
cites work: Q5628266
cites work: Q4053768
cites work: Q3313975
cites work: The torsion of the group of 0-cycles modulo rational equivalence
cites work: ON CONIC BUNDLE STRUCTURES
cites work: FIVE LECTURES ON THREE-DIMENSIONAL VARIETIES
cites work: The middle Jacobian of three-dimensional varieties
description: scientific article; zbMATH DE number 3946314