On compact orbits in singular Kähler spaces
type: Item
instance of: scholarly article
title: On compact orbits in singular Kähler spaces
zbMATH Open document ID: 0903.32009
author: Jörg Winkelmann
published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
publication date: 1999-01-05T00:00:00Z
full work available at URL: https://eudml.org/doc/244153
review text: Given a solvable complex Lie group \(G\) which acts holomorphically on a compact Kähler manifold \(X\), there exists a subtorus \(T\) of the Albanese variety \(Alb (X)\) such that every closed orbit is a torus isogenous to \(T\). The preceding result as pointed out by the author was generalized to singular Kähler spaces in the paper. Recall that a compact complex space \(X\) is of class \({\mathcal C}\) if \(X\) is bimeromorphic to a compact Kähler manifold. The theorem proved here asserts that if \(X\) is of class \({\mathcal C}\) and \(G\) a solvable complex Lie group acting on \(X\), then any two compact \(G\)-orbits are tori isogenous to each other and furthermore isogenous to the \(G\)-orbits in the Albanese of any equivariant desingularization of \(X\).
reviewed by: I-Hsun Tsai
Mathematics Subject Classification ID: 32M05
Mathematics Subject Classification ID: 22E25
zbMATH DE Number: 1089885
zbMATH Keywords: singular Kähler space
zbMATH Keywords: solvable complex Lie group
zbMATH Keywords: Albanese variety
zbMATH Keywords: torus
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description: scientific article; zbMATH DE number 1089885