Point and line arrangements in the plane arise in various contexts, including topology (Zariski pairs), algebra (freeness), and combinatorics. Notably, Hirzebruch utilized these configurations to construct specific ball-quotient surfaces. In this talk, I will introduce operators acting on these arrangements and their corresponding parameter spaces. We shall see how certain elliptic modular surfaces and modular curves can be recovered as parameter spaces of point arrangements under the action of these operators.