Lê's polyhedron for line singularities

Details Lê's polyhedron for line singularities Lê's polyhedron for line singularities

2012-02-05

arxiv.org/abs/1202.0985v1

Mathematics

Complex Variables

Scientific paper

We study the topology of a line singularity, which is a complex hypersurface with non-isolated singularity given by a smooth curve, by means of the description of the degeneration of its Milnor fibre to the singular variety. We construct a polyhedron $P_t$ in $\mathring{X_t}$, the interior of the Milnor fibre, a polyhedron $P_0$ in $\mathring{X_0}$, the interior of the singular fibre, and a continuous map taking $\mathring{X_t}$ to $\mathring{X_0}$ and $P_t$ to $P_0$, which restricts to a homeomorphism outside these polyhedra.

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