Complexity of holomorphic maps from the complex unit ball to classical domains

TL;DR

This paper investigates the complexity and classification of holomorphic maps from the complex unit ball to classical domains, focusing on degree estimates, inequivalence, and explicit examples of proper maps.

Contribution

It provides new degree bounds, constructs a family of inequivalent isometries, and offers examples of non-isometric proper maps, advancing understanding of holomorphic maps between these domains.

Findings

Degree estimates for holomorphic isometries

Construction of a family of inequivalent isometries

Examples of non-isometric proper holomorphic maps

Abstract

We study the complexity of holomorphic isometries and proper maps from the complex unit ball to type IV classical domains. We investigate on degree estimates of holomorphic isometries and holomorphic maps with minimum target dimension. We also construct a real-parameter family of mutually inequivalent holomorphic isometries from the unit ball to type IV domains. We also provide examples of non-isometric proper holomorphic maps from the complex unit ball to classical domains.