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The ultrametric space of plane branches
dc.contributor.author | Abío Roig, Ignasi |
dc.contributor.author | Alberich Carramiñana, Maria |
dc.contributor.author | González Alonso, Víctor |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I |
dc.date.accessioned | 2012-02-10T09:47:39Z |
dc.date.available | 2012-02-10T09:47:39Z |
dc.date.created | 2011 |
dc.date.issued | 2011 |
dc.identifier.citation | Abío, I.; Alberich, M.; Gonzalez, V. The ultrametric space of plane branches. "Communications in algebra", 2011, vol. 39, núm. 11, p. 4206-4220. |
dc.identifier.issn | 0092-7872 |
dc.identifier.uri | http://hdl.handle.net/2117/15048 |
dc.description.abstract | We 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] ∩ 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.extent | 15 p. |
dc.language.iso | eng |
dc.rights | Attribution-NonCommercial-NoDerivs 3.0 Spain |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística |
dc.subject.lcsh | Curves, Plane |
dc.title | The ultrametric space of plane branches |
dc.type | Article |
dc.subject.lemac | Corbes planes |
dc.subject.lemac | Singularitats (Matemàtica) |
dc.contributor.group | Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions |
dc.identifier.doi | 10.1080/00927872.2010.521934 |
dc.description.peerreviewed | Peer Reviewed |
dc.subject.ams | Classificació AMS::14 Algebraic geometry::14H Curves |
dc.subject.ams | Classificació AMS::32 Several complex variables and analytic spaces::32S Singularities |
dc.relation.publisherversion | http://www.tandfonline.com/doi/abs/10.1080/00927872.2010.521934 |
dc.rights.access | Restricted access - publisher's policy |
local.identifier.drac | 9512943 |
dc.description.version | Postprint (published version) |
local.citation.author | Abío, I.; Alberich, M.; Gonzalez, V. |
local.citation.publicationName | Communications in algebra |
local.citation.volume | 39 |
local.citation.number | 11 |
local.citation.startingPage | 4206 |
local.citation.endingPage | 4220 |
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