On tangency in equisingular families of curves and surfaces
| Autor: | Otoniel Nogueira da Silva, Arturo Giles Flores, Jawad Snoussi |
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| Rok vydání: | 2019 |
| Předmět: |
Surface (mathematics)
Pure mathematics Mathematics - Complex Variables General Mathematics Tangent Context (language use) Parameter space Mathematics - Algebraic Geometry FOS: Mathematics Gravitational singularity Complex Variables (math.CV) Topological conjugacy Constant (mathematics) Algebraic Geometry (math.AG) Mathematics |
| DOI: | 10.48550/arxiv.1905.05153 |
| Popis: | We study the behavior of limits of tangents in topologically equivalent spaces. In the context of families of generically reduced curves, we introduce the $s$-invariant of a curve and we show that in a Whitney equisingular family with the property that the $s$-invariant is constant along the parameter space, the number of tangents of each curve of the family is constant. In the context of families of isolated surface singularities, we show through examples that Whitney equisingularity is not sufficient to ensure that the tangent cones of the family are homeomorphic. We explain how the existence of exceptional tangents is preserved by Whitney equisingularity but their number can change. |
| Databáze: | OpenAIRE |
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