  We define a new class of completions of locally symmetric varieties of type
IV which interpolates between the Baily-Borel compactification and Mumford's
toric compactifications. An arithmetic arrangement in a locally symmetric
variety of type IV determines such a completion canonically. This completion
admits a natural contraction that leaves the complement of the arrangement
untouched. The resulting completion of the arrangement complement is very much
like a Baily-Borel compactification: it is the proj of an algebra of
meromorphic automorphic forms. When that complement has a moduli space
interpretation, then what we get is often a compactification obtained by means
of geometric invariant theory. We illustrate this with several examples: moduli
spaces of polarized $K3$ and Enriques surfaces and the semi-universal
deformation of a triangle singularity.
  We also discuss the question when a type IV arrangement is definable by an
automorphic form.
