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Título

The ultrametric space of plane branches

AutorAbío, Ignasi; Alberich-Carramiñana, Maria ; González-Alonso, Víctor
Palabras claveUltrametric distance
Equisingularity class
Plane branch
Fecha de publicación2011
EditorTaylor & Francis
CitaciónCommunications in Algebra 39(11): 4206-4220 (2011)
ResumenWe study properties of the space of irreducible germs of plane curves (branches), seen as an ultrametric space. We provide various geometrical methods to measure the distance between two branches and to compare distances between branches, in terms of topological invariants of the singularity which comprises some of the branches. We show that, in spite of being very close to the notion of intersection multiplicity between two germs, this notion of distance behaves very differently. For instance, any value in [0, 1] ¿ Q is attained as the distance between a fixed branch and some other branch, in contrast with the fact that the semigroup of the fixed branch has gaps. We also present results that lead to interpret this distance as a sort of geometric distance between the topological equivalence or equisingularity classes of branches.
Versión del editorhttp://dx.doi.org/10.1080/00927872.2010.521934
URIhttp://hdl.handle.net/10261/96882
DOI10.1080/00927872.2010.521934
Identificadoresdoi: 10.1080/00927872.2010.521934
issn: 0092-7872
e-issn: 1532-4125
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