On certain complex surface singularities

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 András Némethi. 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.

Eötvös Loránd University PhD thesis. Contains mostly the results of arXiv:1404.2853 and arXiv:1902.01229. Adviser: Prof. András Némethi