Decomposition of compact complex varieties and the cancellation problem
type: Item
instance of: scholarly article
title: Decomposition of compact complex varieties and the cancellation problem
zbMATH Open document ID: 0539.32003
DOI: 10.1007/BF01456081
author: Camilla Horst
published in: Mathematische Annalen
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/163981
review text: Let \({\mathcal T}_ n\) consist of all compact complex varieties of the form \(T\times F/graph \chi\), where \(T={\mathbb{C}}^ n/\Gamma\) is an n-dimensional torus, F a compact complex variety, and \(\chi\) a homomorphism of some finite subgroup of T into Aut(F). The main results of this paper are the following: Cancellation theorem. Let X,Y,Z be compact complex varieties such that \(X\times Z\cong Y\times Z.\) If \(\{\) X,Y,\(Z\} \not\subset {\mathcal T}_ n\) for all \(n>0\), then \(X\cong Y\). - In particular, every \(Z\not\in \cup_{n>0}{\mathcal T}_ n\) cancels. Decomposition theorem. Let X be a compact complex variety which is not contained in any \({\mathcal T}_ n\), \(n>0\). Then X admits a unique decomposition \(X\cong X_ 1\times...\times X_ k\) into indecomposable positive-dimensional factors.
Mathematics Subject Classification ID: 32A07
Mathematics Subject Classification ID: 32M10
Mathematics Subject Classification ID: 32J99
zbMATH DE Number: 3857473
zbMATH Keywords: decomposition of compact complex varieties
zbMATH Keywords: cancellation problem
MaRDI profile type: Publication
cites work: Sur la simplification par les variétés homogenes
cites work: Le problème des modules pour les sous-espaces analytiques compacts d'un espace analytique donné
cites work: Cancellation problem of complete varieties
cites work: Compact varieties of surjective holomorphic endomorphisms
cites work: Sur la simplification par les tores complexes.
cites work: Q4192187
cites work: On the cancellation problem for projective varieties
cites work: Holomorphic automorphisms and cancellation theorems
description: scientific article; zbMATH DE number 3857473