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Search: MSC category 32S30 ( Deformations of singularities; vanishing cycles [See also 14B07] )

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1. CJM Online first

Adamus, Janusz; Seyedinejad, Hadi
Finite determinacy and stability of flatness of analytic mappings
It is proved that flatness of an analytic mapping germ from a complete intersection is determined by its sufficiently high jet. As a consequence, one obtains finite determinacy of complete intersections. It is also shown that flatness and openness are stable under deformations.

Keywords:finite determinacy, stability, flatness, openness, complete intersection
Categories:58K40, 58K25, 32S05, 58K20, 32S30, 32B99, 32C05, 13B40

2. CJM 2005 (vol 57 pp. 3)

Alberich-Carramiñana, Maria; Roé, Joaquim
Enriques Diagrams and Adjacency of Planar Curve Singularities
We study adjacency of equisingularity types of planar complex curve singularities in terms of their Enriques diagrams. The goal is, given two equisingularity types, to determine whether one of them is adjacent to the other. For linear adjacency a complete answer is obtained, whereas for arbitrary (analytic) adjacency a necessary condition and a sufficient condition are proved. We also obtain new examples of exceptional deformations, {\em i.e.,} singular curves of type $\mathcal{D}'$ that can be deformed to a curve of type $\mathcal{D}$ without $\mathcal{D}'$ being adjacent to $\mathcal{D}$.

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