Proper holomorphic mappings between hyperbolic product manifolds

TL;DR

This paper characterizes the structure of finite proper holomorphic maps between hyperbolic product manifolds, extending classical results by combining ideas from Remmert, Stein, and a finiteness theorem for Riemann surfaces.

Contribution

It provides a comprehensive structure theorem for proper holomorphic mappings between hyperbolic product manifolds, generalizing previous special cases.

Findings

Established a structure theorem for proper holomorphic maps

Extended classical results to product of hyperbolic Riemann surfaces

Combined techniques from Remmert, Stein, and finiteness theorems

Abstract

We prove a result on the structure of finite proper holomorphic mappings between complex manifolds that are products of hyperbolic Riemann surfaces. While an important special case of our result follows from the ideas developed by Remmert and Stein, the proof of the full result relies on the interplay of the latter ideas and a finiteness theorem for Riemann surfaces.