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arxiv: math/0611699 · v1 · submitted 2006-11-22 · 🧮 math.CV · math.AG

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Topological Triviality of Families of Singular Surfaces

R. Callejas-Bedregal , K. Houston , M. A. S. Ruas
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classification 🧮 math.CV math.AG
keywords topologicaltrivialityfamiliessingularsurfacescharacterizesconstancydetermined
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We study the topological triviality of families of singular surfaces in ${\mathbb C}^3$ parametrized by $\mathcal A$-finitely determined map germs. We prove that the constancy of the Milnor number of the double point locus characterizes the topological triviality of the family.

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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Equisingularity in families of double point curves

    math.AG 2026-05 unverdicted novelty 6.0

    Authors compare equisingularity of unfoldings and double point curve families, give counterexamples, introduce Henry-type families, and generalize classical formulas to higher-dimensional map germs.