On certain complex surface singularities
@article{Pintr2019OnCC, title={On certain complex surface singularities}, author={Gergo Pint{\'e}r}, journal={arXiv: Algebraic Topology}, year={2019} }
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 Andras Nemethi. 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…
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Cross-caps, triple points and a linking invariant for finitely determined germs
- ArtRevista Matemática Complutense
- 2023
<jats:p>It was recently proved that for finitely determined germs <jats:inline-formula><jats:alternatives><jats:tex-math>$$ \Phi : ( \mathbb C^2, 0) \rightarrow ( \mathbb C^3, 0)…
References
SHOWING 1-10 OF 66 REFERENCES
The boundary of the Milnor fibre of certain non-isolated singularities
- MathematicsPeriod. Math. Hung.
- 2018
This paper provides the plumbing graph of the boundary of the Milnor fibre of f from the double-point-geometry of Phi, a finitely determined complex analytic germ.
Immersions associated with holomorphic germs
- Mathematics
- 2014
A holomorphic germ \Phi: (C^2, 0) \to (C^3, 0), singular only at the origin, induces at the links level an immersion of S^3 into S^5. The regular homotopy type of such immersions are determined by…
The signature of smoothings of complex surface singularities
- Mathematics
- 1978
Let f : (1~3, 0)-"~(t~, 0) be the germ of a complex analytic function with an isolated critical point at the origin. For e > 0 suitably small and 6 yet smaller, the space V ' = f l ( 6 ) ~ D , (where…
The boundary of the Milnor fiber of Hirzebruch surface singularities
- Mathematics
- 2005
We give the first (as far as we know) complete description of the boundary of the Milnor fiber for some non-isolated singular germs of surfaces in ${\bf C}^3$. We study irreducible (i.e. $gcd (m,k,l)…
Some remarks on the geometry and classification of germs of maps from surfaces to 3-space
- Mathematics
- 1987
The boundary of the Milnor fibre of complex and real analytic non-isolated singularities
- Mathematics
- 2011
Let $$f$$f and $$g$$g be holomorphic function-germs vanishing at the origin of complex analytic germs of dimension three. Suppose that they have no common irreducible component and that the real…
Isolated Singular Points on Complete Intersections
- Mathematics
- 1984
This monograph gives a coherent account of the theory of isolated singularities of complete intersections. One encounters such singularities often as the central fibres of analytic map-germs; that is…
Three-Dimensional Link Theory and Invariants of Plane Curve Singularities.
- Mathematics
- 1986
This book gives a new foundation for the theory of links in 3-space modeled on the modern developmentby Jaco, Shalen, Johannson, Thurston et al. of the theory of 3-manifolds. The basic construction…
Regular homotopy classes of immersions of 3-manifolds into 5-space
- Mathematics
- 2002
Abstract We give geometric formulae which enable us to detect (completely in some cases) the regular homotopy class of an immersion with trivial normal bundle of a closed oriented 3-manifold into…