Puiseux power series solutions for systems of equations

Details Puiseux power series solutions for systems of equations Puiseux power series solutions for systems of equations

2008-11-04

arxiv.org/abs/0811.0414v2

Mathematics

Algebraic Geometry

19 pages. To appear in International Journal of Mathematics. Major changes: Several sections added explaining the geometrical

Scientific paper

We give an algorithm to compute term by term multivariate Puiseux series expansions of series arising as local parametrizations of zeroes of systems of algebraic equations at singular points. The algorithm is an extension of Newton's method for plane algebraic curves replacing the Newton polygon by the tropical variety of the ideal generated by the system. As a corollary we deduce a property of tropical varieties of quasi-ordinary singularities.

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