# On certain complex surface singularities

## TL;DR

This paper studies complex surface singularities arising from holomorphic germs, focusing on finitely determined cases, and develops algorithms and theoretical links between singularity and immersion theories.

## Contribution

It introduces new methods for analyzing finitely determined germs and their Milnor fibers, connecting complex singularity theory with immersion theory.

## Key findings

- Analysis of the immersion $S^3 o S^5$ related to surface singularities
- Development of an algorithm for Milnor fiber boundary determination
- Bridges established between singularity and immersion theories

## Abstract

The thesis deals with holomorphic germs $ \Phi: (\mathbb{C}^2, 0) \to (\mathbb{C}^3,0) $ singular only at the origin, with a special emphasis on the distinguished class of finitely determined germs. The results are published in two articles (arXiv:1404.2853 and arXiv:1902.01229), joint with Andr\'{a}s N\'{e}methi. In Chapter 3 of the thesis we study the associated immersion $ S^3 \looparrowright S^5 $, while Chapter 5 contains an algorithm providing the Milnor fibre boundary of the non-isolated hypersurface singularity determined by the image of $ \Phi $. These results create bridges between different areas of complex singularity theory and immersion theory. The background of these topics is summerized in Chapter 1, 2 and 4.