On the Picard group of a compact complex nilmanifold
type: Item
instance of: scholarly article
title: On the Picard group of a compact complex nilmanifold
zbMATH Open document ID: 0542.14032
DOI: 10.1216/RMJ-1983-13-4-631
author: Robert J. jun. Fisher
published in: Rocky Mountain Journal of Mathematics
publication date: 1983-01-01T00:00:00Z
review text: A nilmanifold \(X=G/\Gamma\) is the compact quotient of a nilpotent simply connected Lie group G by a lattice \(\Gamma\). (Examples: tori are the only Kähler ones.) This paper proves, in particular, that if \(\pi:X\to T\) is the Albanese map of X, then \(\pi^*:Pic^ 0(T)\to Pic^ 0(X)\) is biholomorphic, and that \(Pic^ 0(X)\) is of finite index in the kernel of the Bockstein map \(\delta:H^ 1(X,{\mathcal O}^*)\to H^ 2(G/\Gamma,{\mathbb{Z}}).\)
Mathematics Subject Classification ID: 14M17
Mathematics Subject Classification ID: 14C22
Mathematics Subject Classification ID: 32M10
Mathematics Subject Classification ID: 32J25
Mathematics Subject Classification ID: 22E25
Mathematics Subject Classification ID: 14L30
zbMATH DE Number: 3861337
zbMATH Keywords: nilmanifold
zbMATH Keywords: quotient of a nilpotent simply connected Lie group
zbMATH Keywords: Bockstein map
reviewed by: Frédéric Campana
MaRDI profile type: Publication
full work available at URL: rmj-1983-13-4-631
OpenAlex ID: W2025196640
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description: scientific article; zbMATH DE number 3861337