CEU Electronic Theses and Dissertations, 2023
| Author | Sándor, András |
|---|---|
| Title | Non-isolated Surface Singularities |
| Summary | This thesis includes two results about non-isolated complex surface singularities. First, it was recently proved that for finitely determined germs $ \Phi: ( \C^2, 0) \to ( \C^3, 0) $, the number $C(\Phi)$ of Whitney umbrella points and the number $T(\Phi)$ of triple values of a stable deformation are topological invariants. The proof uses the fact that the combination $C(\Phi)-3T(\Phi)$ is topological since it equals the linking invariant of the associated immersion $S^3 \looparrowright S^5$ introduced by Ekholm and Sz\H{u}cs. We provide a new, direct proof for this equality. We also clarify the relation between various definitions of the linking invariant. Second, we know that the Milnor fibre boundary of an isolated complex surface singularity has a graph manifold structure. We define a family of non-isolated toric surface singularities by introducing gaps to the semigroups corresponding to cyclic quotinet singularites. Then we give a singular Milnor fibration for them via one-parameter toric deformations. We describe the Milnor fibre boundaries as graph manifolds. We also develop the theoretical background and language needed for these results including theory of analytic singularities, deformations, map germs and affine toric varieties. |
| Supervisor | Némethi, András |
| Department | Mathematics PhD |
| Full text | https://www.etd.ceu.edu/2023/sandor_andras.pdf |
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