CR TRANSVERSALITY OF HOLOMORPHIC MAPPINGS BETWEEN GENERIC SUBMANIFOLDS IN COMPLEX SPACES.

We show that a holomorphic mapping sending one generic submanifold into another of the same dimension is CR transversal to the target submanifold provided that the source manifold is of finite type and the map is of generic full rank. This result and its corollaries completely resolve two questions posed by Linda P. Rothschild and the first author in 2006. Another one of our main results, in the special setting of hypersurfaces, was also explicitly stated as a conjecture by B. Lamel and N. Mir in a paper from 2006. [ABSTRACT FROM AUTHOR]