Point configurations and translations

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• 作者：Hendrik B?ker
• 关键词：14L24 ; 14L30
• 刊名：manuscripta mathematica
• 出版年：2015
• 出版时间：January 2015
• 年：2015
• 卷：146
• 期：1-2
• 页码：235-263
• 全文大小：395 KB
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• 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

The spaces of point configurations on the projective line up to the action of \({{\rm SL}(2,\mathbb{K})}\) and its maximal torus are canonically compactified by the Grothdieck–Knudsen and Losev–Manin moduli spaces \({\overline{M}_{0,n}}\) and \({\overline{L}_n}\) respectively. We examine the configuration space up to the action of the maximal unipotent group \({\mathbb{G}_a \subseteq {\rm SL}(2,,\mathbb{K})}\) and define an analogous compactification. For this we first assign a canonical quotient to the action of a unipotent group on a projective variety. Moreover, we show that similar to \({\overline{M}_{0,n}}\) and \({\overline{L}_n}\) this quotient arises in a sequence of blow-ups from a product of projective spaces.