Approximation of Holomorphic Solutions of a system of Real Analytic Equations

Michel Hickel (1) , Guillaume Rond (2)

1 IMB - Institut de Mathématiques de Bordeaux
2 I2M - Institut de Mathématiques de Marseille

We prove the existence of an approximation function for holomorphic solutions of a system of real analytic equations. For this we use ultraproducts and Weierstras systems introduced by J. Denef and L. Lipshitz. We also prove a version of the Ploski smoothing theorem in this case.

Mots clés: real analytic equations; Artin Approximation; real analytic equations.

Domaines: Géométrie algébrique [math.AG]

Michel Hickel, Guillaume Rond. Approximation of Holomorphic Solutions of a system of Real Analytic Equations. Canad. Math. Bull, 2012, 55 (4), pp.752-761. ⟨10.4153/CMB-2011-129-4⟩. ⟨hal-00772762⟩