An explicit description of the relative \({SL_{4}(\mathbb{C})}\) -character variety of the projective line

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• 作者：Arata Komyo
• 刊名：manuscripta mathematica
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：150
• 期：3-4
• 页码：441-464
• 全文大小：670 KB
• 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
• 卷排序：150

文摘

In this paper, we give an explicit description of a certain character variety of dimension 2, and we construct a compactification of the character variety. We show that the compactification is a del Pezzo surface. One motivation of the explicit description is investigation of the mixed Hodge structure of the character variety. For the character variety, we can verify some conjectures on the mixed Hodge structures and the configurations of the boundaries of compactifications.Mathematics Subject Classification14L2414L30