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Generalized Newton-Puiseux Theory and Hensel's Lemma in C[[x, y]]

Published online by Cambridge University Press:  20 November 2018

Tzee-Char Kuo
Tzee-Char Kuo*
Affiliation:
University of Sydney, Sydney, Australia
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The Newton polygon and the Newton-Puiseux algorithm ([3], p. 370, [8], p. 98), and their generalizations, serve as a powerful tool for analysing the singularities of a given function. Yet experts know how difficult it is to keep track of them when one, or several, blowing-ups are applied. Thus many interesting theorems are stated under the strong, rather undesirable, assumption that the Newton faces are non-degenerate.

In this paper, we introduce a method which is parallel to the classical Newton-Puiseux theory, yet avoids blowing-ups and fractional power series, except in the proofs.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 41 , Issue 6 , 01 December 1989 , pp. 1101 - 1116
Copyright
Copyright © Canadian Mathematical Society 1989

References

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