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Seeking invariants for blow-analytic equivalence. (English) Zbl 0873.32008

T.-C.Kuo introduced the notion of blow-analytic equivalence, and proved a satisfactory finite classification theorem [T.-C. Kuo, Invent. Math. 82, 257-262 (1985; Zbl 0587.32018)]. In [T.-C. Kuo, J. Math. Soc. Japan 32, 605-614 (1980; Zbl 0509.58007); T. Fukui and E. Yoshinaga, Invent. Math. 82, 467-477 (1985; Zbl 0559.58005); T. Fukui, J. Math. Soc. Japan 44, No. 3, 455-459 (1992; Zbl 0766.58008)], some theorems were proved which assert that several families are blow-analytically trivial. The next problem is to find criteria that two function-germs are not blow-analytically equivalent.
The author introduces some blow-analytic invariants of real analytic function-germs and discusses their properties. As a consequence, it is obtained, for instance, that the multiplicity of function-germs is a blow-analytic invariant.

MSC:

32C07 Real-analytic sets, complex Nash functions
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