Covering relations between ball-quotient orbifolds

Abstract

Some ball-quotient orbifolds are related by covering maps. We exploit these coverings to find infinite towers of orbifolds uniformized by the complex 2-ball and some orbifolds over K3 surfaces uniformized by the 2-ball. Corresponding lattices are all arithmetic and commensurable. We also give, along with infinitely many reducible examples, an infinite series of irreducible curves along which the projective plane is uniformized by the product of two 1-balls.