Łojasiewicz inequality over the ring of power series in two variables

Guillaume Rond (1)

1 I2M - Institut de Mathématiques de Marseille

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.

Domaines: Algèbre commutative [math.AC]

Guillaume Rond. Łojasiewicz inequality over the ring of power series in two variables. Mathematical Research Letters, 2013, ⟨10.4310/MRL.2013.v20.n2.a9⟩. ⟨hal-01255234⟩