Complex-analytic quotients of algebraic \(G\) -varieties

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• 作者：Daniel Greb
• 关键词：32M05 ; 14L24 ; 14L30
• 刊名：Mathematische Annalen
• 出版年：2015
• 出版时间：October 2015
• 年：2015
• 卷：363
• 期：1-2
• 页码：77-100
• 全文大小：562 KB
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• 作者单位：Daniel Greb (1)
  
  1. Essener Seminar für Algebraische Geometrie und Arithmetik, Fakult?t für Mathematik, Universit?t Duisburg-Essen, 45117, Essen, Germany
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-1807

文摘

It is shown that any compact semistable quotient of a normal variety by a complex reductive Lie group \(G\) (in the sense of Heinzner and Snow) is a good quotient. This reduces the investigation and classification of such complex-analytic quotients to the corresponding questions in the algebraic category. As a consequence of our main result, we show that every compact space in Nemirovski’s class \(\fancyscript{Q}_G\) has a realisation as a good quotient, and that every complete algebraic variety in \(\fancyscript{Q}_G\) is unirational with finitely generated Cox ring and at worst rational singularities. In particular, every compact space in class \(\fancyscript{Q}_T\), where \(T\) is an algebraic torus, is a toric variety. Mathematics Subject Classification 32M05 14L24 14L30