A relative Hilbert–Mumford criterion

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• 作者：Martin G. Gulbrandsen ; Lars H. Halle ; Klaus Hulek
• 关键词：14L24 (primary) ; 13A50 ; 14D06 (secondary)
• 刊名：manuscripta mathematica
• 出版年：2015
• 出版时间：November 2015
• 年：2015
• 卷：148
• 期：3-4
• 页码：283-301
• 全文大小：495 KB
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• 作者单位：Martin G. Gulbrandsen (1)
  Lars H. Halle (2)
  Klaus Hulek (3) (4)
  
  1. Department of Mathematics and Natural Sciences, University of Stavanger, 4036, Stavanger, Norway
  2. Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100, Copenhagen, Denmark
  3. Institut für Algebraische Geometrie, Leibniz Universit?t Hannover, Welfengarten 1, 30060, Hannover, Germany
  4. Institute for Advanced Study, School of Mathematics, 1 Einstein Drive, Princeton, NJ, 08540, USA
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Algebraic Geometry
  Topological Groups and Lie Groups
  Geometry
  Number Theory
  Calculus of Variations and Optimal Control
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-1785

文摘

We generalize the classical Hilbert–Mumford criteria for GIT (semi-)stability in terms of one parameter subgroups of a linearly reductive group G over a field k, to the relative situation of an equivariant, projective morphism \({X \rightarrow \,{\rm Spec}\,\, A}\) to a noetherian k-algebra A. We also extend the classical projectivity result for GIT quotients: the induced morphism \({X^{ss} /G \rightarrow \,{\rm Spec}\,\, A^G}\) is projective. As an example of applications to moduli problems, we consider degenerations of Hilbert schemes of points. Mathematics Subject Classification 14L24 (primary) 13A50 14D06 (secondary)