  Integrable lattice equations arising in the context of singular manifold
equations for scalar, multicomponent KP hierarchies and 2D Toda lattice
hierarchy are considered. These equation generate the corresponding continuous
hierarchy of singular manifold equations, its B\"acklund transformations and
different forms of superposition principles. They possess rather special form
of compatibility representation. The distinctive feature of these equations is
invariance under the action of M\"obius transformation. Geometric
interpretation of these discrete equations is given.
