2026/07/21 by Cindy Tan
Mathematics · #math.GT #math.AG #math.DG
In 1986, Deligne and Mostow constructed a ball quotient \mathbbB2 / Γ biholomorphic to the complex projective plane ℙ2 whose branch locus is a line arrangement. In this paper, we show that if ℙ2 is realized as a ball quotient whose branch divisor D is an arrangement of smooth pairwise normal-crossing curves, then the orbifold (ℙ2,D) is isomorphic to either the Deligne-Mostow example or a certain degree 9 cover of it. This classification of "ball quotient structures" on ℙ2 generalizes the ℙ1 case due to Poincaré.