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Transactions of the American Mathematical Society

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Analytic equations and singularities of plane curves


Author: John J. Wavrik
Journal: Trans. Amer. Math. Soc. 245 (1978), 409-417
MSC: Primary 14D15
DOI: https://doi.org/10.1090/S0002-9947-1978-0511419-5
MathSciNet review: 511419
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Abstract: Theorems (Artin, Wavrik) exist which show that sufficiently good approximate (power series) solutions to a system of analytic equations may be approximated by convergent solutions. This paper considers the problem of explicity determining the order, $ \beta $, to which an approximate solution must solve the system of equations.

The paper deals with the case of one equation, $ f(x,y) = 0$, in two variables. It is shown how $ \beta $ depends on the singularities of the curve $ f(x,y) = 0$. A method for obtaining the minimal $ \beta $ is given. A rapid way of finding $ \beta $ using the Newton Polygon for f applies in special cases.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1978-0511419-5
Keywords: Analytic equations, plane curve singularities, power series, algebraic functions
Article copyright: © Copyright 1978 American Mathematical Society

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