CR transversality of holomorphic mappings between generic submanifolds in complex spaces

摘要

We show that a holomorphic mapping sending one generic submanifold intoanother of the same dimension is CR transversal to the target submanifoldprovided that the source manifold is of finite type and the map is of genericfull rank. This result and its corollaries completely resolve two questionsposed by Linda P. Rothschild and the first author in a paper from 2006.