Stability of Newton boundaries of a family of real analytic singularities

Author:
Masahiko Suzuki

Journal:
Trans. Amer. Math. Soc. **323** (1991), 133-150

MSC:
Primary 32S15; Secondary 58C27

MathSciNet review:
978382

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let be a real analytic -parameter family of real analytic functions defined in a neighborhood of the origin in . Suppose that admits a blow analytic trivilaization along the parameter (see the definition in of this paper). Under this condition, we prove that there is a real analytic -parameter family with and of local coordinates in which the Newton boundaries of are stable. This fact claims that the blow analytic equivalence among real analytic singularities is a fruitful relationship since the Newton boundaries of singularities contains a lot of informations on them.

**[1]**T. Fukui and E. Yoshinaga,*The modified analytic trivialization of family of real analytic functions*, Invent. Math.**82**(1981), 467-477 MR**811547 (87a:58028)****[2]**T. C. Kuo,*The modified analytic trivialization of singularities*, J. Math. Soc. Japan**32**(1980), 605-614 MR**589100 (82d:58012)****[3]**T. C. Kuo and J. N. Ward,*A theorem on almost analytic equisingularities*, J. Math. Soc. Japan**33**(1981), 471-484 MR**620284 (83c:32015)****[4]**T. C. Kuo,*Une classification des singularités réelles*, C.R. Acad. Sci. Paris**288**(1979), 809-812 MR**535641 (80i:32034)****[5]**-,*On classification of real singularities*, Invent. Math.**82**(1985), 257-262 MR**809714 (87d:58025)****[6]**D. T. Le, and C. P. Ramanujan,*The invariance of Milnor's number implies the invariance of the topological types*, Amer. J. Math.**98**(1976), 67-78 MR**0399088 (53:2939)****[7]**M. Oka,*On the stability of the Newton boundary*, Proc. Sympos. Pure Math., vol. 40, Amer. Math. Soc., Providence, R.I., 1983, pp. 259-268 MR**713254 (85i:32031)**

Retrieve articles in *Transactions of the American Mathematical Society*
with MSC:
32S15,
58C27

Retrieve articles in all journals with MSC: 32S15, 58C27

Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9947-1991-0978382-0

Article copyright:
© Copyright 1991
American Mathematical Society