The Bolza Curve and Some Orbifold Ball Quotient Surfaces

Abstract

We study Deraux’s nonarithmetic orbifold ball quotient surfaces obtained as birational transformations of a quotient X of a particular Abelian surface A. Using the fact that A is the Jacobian of the Bolza genus 2 curve, we identify X as the weighted projective plane P(1,3,8). We compute the equation of the mirror M of the orbifold ball quotient (X,M), and by taking the quotient by an involution we obtain an orbifold ball quotient surface with mirror birational to an interesting configuration of plane curves of degrees 1, 2, and 3. We also exhibit an arrangement of four conics in the plane that provides the above-mentioned ball quotient orbifold surfaces.