Carrousel in family and non-isolated hypersurface singularities in $C^3$

Details Carrousel in family and non-isolated hypersurface singularities in $C^3$ Carrousel in family and non-isolated hypersurface singularities in $C^3$

2010-11-30

arxiv.org/abs/1011.6503v1

Mathematics

Algebraic Geometry

33 pages

Scientific paper

We study the boundary $L_t$ of the Milnor fiber for the reduced holomorphic germs $f:(\Bbb C^3,0) \rightarrow (\Bbb C,0)$ having a non-isolated singularity at $0$. We prove that $L_t$ is a graph manifold by using a new technique of carrousel depending on one parameter varying on a circle. Our results enable one to compare the topology of $L_t$ and of the link of the normalization of $f^{-1}(0)$.

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