We construct projective models for Humbert surfaces and QCM-curves, i.e., S
himura curves together with their natural embedding into the coarse moduli
space for principally polarized abelian surfaces. The points of a QCM-curve
correspond to an abelian surface, such that its algebra of complex multipl
ications is an order in an indefinite rational quaternian algebra. Moreover
, we determine the structure of such orders.