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dc.contributor.authorAbío Roig, Ignasi
dc.contributor.authorAlberich Carramiñana, Maria
dc.contributor.authorGonzález Alonso, Víctor
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I
dc.date.accessioned2010-09-16T08:10:02Z
dc.date.available2010-09-16T08:10:02Z
dc.date.issued2010-08
dc.identifier.urihttp://hdl.handle.net/2117/8895
dc.description.abstractWe 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] \cap 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
dc.format.extent16 p.
dc.language.isoeng
dc.relation.ispartofseries[prepr201005AbiAG]
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 Spain
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística
dc.titleThe ultrametric space of plane branches
dc.typeExternal research report
dc.subject.lemacCorbes planes
dc.contributor.groupUniversitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
dc.relation.publisherversionhttp://www.ma1.upc.edu/recerca/preprints/2010/prepr201001alberich.pdf
dc.rights.accessOpen Access
local.identifier.drac2634272
dc.description.versionPreprint
local.personalitzacitaciotrue


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