On germs of mappings $\mathbb C^2\to\mathbb C^2$

TL;DR

This paper characterizes local behavior of complex mappings from a7^2 to a7^2 that are ramified along specific irreducible curves, focusing on those with images of the form x^p=y^q.

Contribution

It provides a detailed description of germs of mappings with ramification along certain irreducible curves and specific image forms, advancing understanding of their local structure.

Findings

Classification of germs ramified along irreducible curves

Description of mappings with image x^p=y^q

Insights into local behavior of complex mappings

Abstract

We describe germs of mappings $(\mathbb{C}^2,0) \to (\mathbb{C}^2,0)$ ramified along a germ of irreducible curve whose image is of the form $x^p=y^q$.