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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

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
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Abstract: Let $ {f_t}(x,y)$ be a real analytic $ t$-parameter family of real analytic functions defined in a neighborhood of the origin in $ {\mathbb{R}^2}$. Suppose that $ {f_t}(x,y)$ admits a blow analytic trivilaization along the parameter $ t$ (see the definition in $ \S1 $ of this paper). Under this condition, we prove that there is a real analytic $ t$-parameter family $ {\sigma _t}(x,y)$ with $ {\sigma _0}(x,y)=(x,y)$ and $ {\sigma _t}(0,0)=(0,0)$ of local coordinates in which the Newton boundaries of $ {f_t}(x,y)$ 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.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1991-0978382-0
Article copyright: © Copyright 1991 American Mathematical Society