Displaying similar documents to “Local embeddings of lines in singular hypersurfaces”

Deformation of polar methods

David B. Massey, Dirk Siersma (1992)

Annales de l'institut Fourier

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We study deformations of hypersurfaces with one-dimensional singular loci by two different methods. The first method is by using the Le numbers of a hypersurfaces singularity — this falls under the general heading of a “polar” method. The second method is by studying the number of certain special types of singularities which occur in generic deformations of the original hypersurface. We compare and contrast these two methods, and provide a large number of examples.

Equisingular generic discriminants and Whitney conditions

Eric Dago Akéké (2008)

Annales de la faculté des sciences de Toulouse Mathématiques

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The purpose of this article is to show that are satisfied for complex analytic families of normal surface singularities for which the are . According to J. Briançon and J. P. Speder the constancy of the topological type of a family of surface singularities does not imply Whitney conditions in general. We will see here that for a family of these two equisingularity conditions are equivalent.

Singularities in drawings of singular surfaces

Alain Joets (2008)

Banach Center Publications

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When drawing regular surfaces, one creates a concrete and visual example of a projection between two spaces of dimension 2. The singularities of the projection define the apparent contour of the surface. As a result there are two types of generic singularities: fold and cusp (Whitney singularities). The case of singular surfaces is much more complex. A priori, it is expected that new singularities may appear, resulting from the "interaction" between the singularities of the surface and...