Let "F" be a totally real number field and "D" a quaternion division algebra over "F". The multiplicative group "D"× gives rise to a canonical Shimura variety. Its dimension "d" is the number of infinite places over which "D" splits. In particular, if "d" = 1 (for example, if "F" = Q and "D" ⊗ R ≅ M2(R)), fixing a sufficiently small arithmetic subgroup of "D"×, one gets a Shimura curve, and curves arising from this construction are already compact (i.e. projective).