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Article Dans Une Revue Journal of Algebraic Geometry Année : 2010

Blow-analytic equivalence of two variable real analytic function germs

Résumé

Blow-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.

Dates et versions

hal-00941043 , version 1 (03-02-2014)

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Citer

Satoshi Koike, Adam Parusinski. Blow-analytic equivalence of two variable real analytic function germs. Journal of Algebraic Geometry, 2010, 19 (3), pp.34. ⟨10.1090/S1056-3911-09-00527-X⟩. ⟨hal-00941043⟩
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