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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
ISSN0747-7171
URL http://www.sciencedirect.com/science/article/pii/S0747717106000666
LanguageEnglish
JournalJournal of Symbolic Computation
Volume42
Number1–2
Pages89 - 114
Year2007
NoteEffective Methods in Algebraic Geometry (MEGA 2005)
Edition0
Translation No
Refereed No
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