Black holes in string theory compactified on Calabi-Yau varieties a priori
might be expected to have moduli dependent features. For example the entropy of
the black hole might be expected to depend on the complex structure of the
manifold. This would be inconsistent with known properties of black holes.
Supersymmetric black holes appear to evade this inconsistency by having moduli
fields that flow to fixed points in the moduli space that depend only on the
charges of the black hole. Moore observed in the case of compactifications with
elliptic curve factors that these fixed points are arithmetic, corresponding to
curves with complex multiplication. The main goal of this talk is to explore
the possibility of generalizing such a characterization to Calabi-Yau varieties
with finite fundamental groups.