The complex projective plane as a ball quotient

In 1986, Deligne and Mostow constructed a ball quotient $\mathbb{B}^2 / Γ$ biholomorphic to the complex projective plane $\mathbb{P}^2$ whose branch locus is a line arrangement. In this paper, we show that if $\mathbb{P}^2$ is realized as a ball quotient whose branch divisor $D$ is an arrangement of