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TitleEquisingular calculations for plane curve singularities
Author(s) Antonio Campillo, Gert-Martin Greuel, Christoph Lossen
TypeArticle in Journal
AbstractWe present an algorithm which, given a deformation with section of a reduced plane curve singularity, computes equations for the equisingularity stratum (that is, the μ -constant stratum in characteristic 0) in the parameter space of the deformation. The algorithm works for any, not necessarily reduced, parameter space and for algebroid curve singularities C defined over an algebraically closed field of characteristic 0 (or of characteristic p > ord ( C ) ). It provides at the same time an algorithm for computing the equisingularity ideal of J. Wahl. The algorithms have been implemented in the computer algebra system Singular. We show them at work by considering two non-trivial examples. As the article is also meant for non-specialists in singularity theory, we include a short survey on new methods and results about equisingularity in characteristic 0.
KeywordsEquisingular deformation, Plane curve singularities, Milnor number, Hamburger–Noether expansion, Deformation of parametrization
URL http://www.sciencedirect.com/science/article/pii/S0747717106000666
JournalJournal of Symbolic Computation
Pages89 - 114
NoteEffective Methods in Algebraic Geometry (MEGA 2005)
Translation No
Refereed No