On Certain Complex Surface Singularities

The thesis deals with holomorphic germs Φ: (ℂ^2, 0) → (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 András Némethi. In Chapter 3 of the thesis we study the associated immersion S^3 ↬ S^5, while Chapter 5 contains an algorithm providing the Milnor fibre boundary of the non-isolated hypersurface singularity determined by the image of Φ. 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.