Families of proper holomorphic maps
Barbara Drinovec Drnovsek, Jure Kalisnik

TL;DR
This paper constructs a continuous family of proper holomorphic maps from a surface with varying complex structures into 2, demonstrating how such maps can depend continuously on parameters.
Contribution
It introduces a method to produce continuous families of proper holomorphic maps from surfaces with varying complex structures into 2.
Findings
Established the existence of continuous families of proper holomorphic maps
Demonstrated dependence of maps on parameter space
Extended previous results to more general surface families
Abstract
Given a smooth, open, oriented surface endowed with a family of complex structures depending continuously on the parameter in a metrisable space , we construct a continuous family of proper holomorphic maps , .
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