On compactifications of character varieties of n-punctured projective line

2013/07/30 by Arata Komyo, Komyo, Arata
Mathematics · #14L24 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #math.AG #msc:14L24

paper · pdf · doi:10.48550/arxiv.1307.7880

23 pages, 3 figures, to appear in Annales de l'Institut Fourier

openalex publication_date 2013/07/30 · arxiv created 2015/01/13 · arxiv updated 2015/01/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this paper, we construct compactifications of SL₂(ℂ)-character varieties of n-punctured projective line and study the boundary divisor of the compactifications. This study is motivated by the conjecture for the configuration of the boundary divisor, due to C. Simpson. We verify the conjecture for a few examples.

Citations

• The invariant theory of n × n matrices

Related

• On compactifications of the SL(2,C) character varieties of punctured surfaces
• The Geometric P=W conjecture and Thurston's compactification
• Poisson structure on character varieties
• The dual boundary complex of the SL₂ character variety of a punctured sphere
• On the character variety of the three-holed projective plane