CR transversality of holomorphic mappings between generic submanifolds in complex spaces

TL;DR

This paper proves that under certain conditions, holomorphic mappings between generic submanifolds in complex spaces are CR transversal, resolving longstanding questions in the field.

Contribution

It establishes CR transversality for holomorphic maps between generic submanifolds of the same dimension, answering two open questions from 2006.

Findings

Holomorphic maps are CR transversal if source is finite type and map has full rank.

Results apply to generic submanifolds in complex spaces.

Complete resolution of two open questions from prior research.

Abstract

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 a paper from 2006.