Abstract
We study the topology of line singularities, which are complex hypersurface germs with non-isolated singularity given by a smooth curve. We describe the degeneration of its Milnor fiber to the singular hypersurface by means of a vanishing polyhedron in the Milnor fiber. As a milestone, we also study the topology of the degeneration of a complex isolated singularity hypersurface under a nonlocal point of view.
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