The Bolza curve and some orbifold ball quotient surfaces

Abstract

We study Deraux's non-arithmetic 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 which provides the abovementioned ball quotient orbifold surfaces. 2010 MSC: 22E40 (14L30 20H15 14J26)