2007/10/04 by Koike, Satoshi, Parusinski, Adam
#14B05 #32S15 #Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.0710.1046
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.