Blow-analytic equivalence of two variable real analytic function germs

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dc.creatorKoike, Satoshi
dc.creatorParusinski, Adam
dc.date2007-10-04
dc.date2008-04-11
dc.date.accessioned2026-07-07T09:31:26Z
dc.date.available2026-07-07T09:31:26Z
dc.descriptionBlow-analytic equivalence is a notion for real analytic function germs, introduced by Tzee-Char Kuo in order to develop real analytic equisingularity theory. In this paper we give complete characterisations of blow-analytic equivalence in the two dimensional case: in terms of the real tree model for the arrangement of real parts of Newton-Puiseux roots and their Puiseux pairs, and in terms of minimal resolutions. These characterisations show that in the two dimensional case the blow-analytic equivalence is a natural analogue of topological equivalence of complex analytic function germs. Moreover, we show that in the two-dimensional case the blow-analytic equivalence can be made cascade, and hence satisfies several geometric properties. It preserves, for instance, the contact orders of real analytic arcs. In the general $n$-dimensional case, we show that a singular real modification satisfies the arc-lifting property.
dc.description7 figures
dc.identifierhttps://arxiv.org/abs/0710.1046
dc.identifierhttp://arxiv.org/abs/0710.1046
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/158454
dc.subjectAlgebraic Geometry
dc.subject32S15; 14B05
dc.titleBlow-analytic equivalence of two variable real analytic function germs
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