  A class of complex hyperbolic lattices in PU(2,1) called the Deligne-Mostow
lattices has been reinterpreted by Hirzebruch and others in terms of line
arrangements. They use branched covers over a suitable blow up of the complete
quadrilateral arrangement of lines in projective 2-space to construct the
complex hyperbolic surfaces over the orbifolds associated to the lattices.
  Fundamental domains for these lattices have been built by Pasquinelli. Here
we show how the fundamental domains can be interpreted in terms of line
arrangements as above. This parallel is then applied in two contexts.
  Dashyan uses Hirzebruch's construction to build infinitely many
representations of 3-manifolds. Here we show that his construction can be
generalised to all of the Deligne-Mostow lattices and more representations can
be built.
  Wells shows that two of the Deligne-Mostow lattices in PU(2,1) can be seen as
hybrids of lattices in PU(1,1). Here we show that he implicitly uses the line
arrangement and we complete his analysis to all possible pairs of lines. In
this way, we show that three more Deligne-Mostow lattices can be given as
hybrids.
