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Topological types of quasi-ordinary singularities

Author: Kyungho Oh
Journal: Proc. Amer. Math. Soc. 117 (1993), 53-59
MSC: Primary 32S50; Secondary 32S05, 32S25
MathSciNet review: 1106181
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Abstract: A germ $ (X,x)$ of a complex analytic hypersurface in $ {\mathbb{C}^{d + 1}}$ is quasi-ordinary if it can be represented as the image of an open neighborhood of 0 in $ {\mathbb{C}^d}$ under the map $ ({s_1}, \ldots ,{s_d}) \mapsto (s_1^n, \ldots ,s_d^n,\zeta ({s_1}, \ldots ,{s_d})),\;n > 0$, where $ \zeta $ is a convergent power series. It is shown that the topological type of the singularity $ (X,x) \subset ({\mathbb{C}^{d + 1}},0)$ is determined by a certain set of fractional monomials, called the characteristic monomials, appearing in the fractional power series $ \zeta (t_1^{1/n}, \ldots ,t_d^{1/n})$.

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Article copyright: © Copyright 1993 American Mathematical Society