On compactifications of character varieties of nn-punctured projective line

In this paper, we construct compactifications of $SL_2(\mathbb{C})$-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.Comment: 23 pages, 3 figures, to appear in Annales de l'Institut Fourie