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Enriques Diagrams and Adjacency of Planar Curve Singularities

Published online by Cambridge University Press:  20 November 2018

Maria Alberich-Carramiñana
Affiliation:
Departament de Matemàtica Aplicada I, Universitat Politècnica de Catalunya, Av. Diagonal 647, 08028-Barcelona, Spain E-mail: [email protected]
Joaquim Roé
Affiliation:
Departament de Matemàtiques, Universitat Autonòma de Barcelona, Edifici C, 08193-Bellaterra, Barcelona, Spain e-mail: [email protected]
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Abstract

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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 themis 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, 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 $\mathcal{D}$.

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2005

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