Models of 2-nondegenerate CR hypersurface in CN

We show that every point in a uniformly 2-nondegenerate CR hypersurface is canonically associated with a model 2-nondegenerate structure. The 2-nondegenerate models are basic CR invariants playing the same fundamental role as quadrics do in the Levi nondegenerate case. We characterize all 2-nondegenerate models and show that the moduli space of such hypersurfaces in CN is infinite dimensional for each N>3. We derive a normal form for these models' defining equations that is unique up to an action of a finite dimensional Lie group. We generalize recently introduced CR invariants termed modified symbols, and show how to compute these intrinsically defined invariants from a model's defining equation. We show that these models automatically possess infinitesimal symmetries spanning a complement to their Levi kernel and derive explicit formulas for them.