On the classification of rational sphere maps

TL;DR

This paper introduces a new classification framework for rational sphere maps between complex spheres, utilizing Hermitian forms and a novel ancestor-descendant hierarchy to analyze their structure.

Contribution

It provides a new classification result for CR rational maps between spheres, employing Hermitian forms and a hierarchical ancestor-descendant approach.

Findings

Established a classification scheme for rational sphere maps

Introduced the concepts of ancestors and descendants in this context

Enhanced understanding of the structure of CR rational maps

Abstract

We prove a new classification result for (CR) rational maps from the unit sphere in some ${\mathbb C}^n$ to the unit sphere in ${\mathbb C}^N$. To so so, we work at the level of Hermitian forms, and we introduce ancestors and descendants.