Analytic equations and singularities of plane curves

Author:
John J. Wavrik

Journal:
Trans. Amer. Math. Soc. **245** (1978), 409-417

MSC:
Primary 14D15

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, , to which an approximate solution must solve the system of equations.

The paper deals with the case of one equation, , in two variables. It is shown how depends on the singularities of the curve . A method for obtaining the minimal is given. A rapid way of finding using the Newton Polygon for *f* applies in special cases.

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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