Mathematical Research Letters

Volume 20 (2013)

Number 2

Łojasiewicz inequality over the ring of power series in two variables

Pages: 325 – 337

DOI: http://dx.doi.org/10.4310/MRL.2013.v20.n2.a9

Author

Guillaume Rond (Institut de Mathématiques de Luminy, Faculté des Sciences de Luminy, Marseille, France)

Abstract

We prove a Łojasiewicz type inequality for a system of polynomial equations with coefficients in the ring of formal power series in two variables. This result is an effective version of the Strong Artin Approximation Theorem. From this result, we deduce a bound of Artin functions of isolated singularities.

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