# Calcul de la fonction d'Artin d'une singularité plane

Abstract : Let K be an algebraically closed field of characteristic zero, and let A = K[[t1, . . . , tN]], N>0 be the ring of formal power series in t1, . . .,tN with coefficients in K. Let I = (f1, . . . , fp) be a nonzero ideal of the ring A[[x1, . . . , xe]] of formal power series in x1, . . . , xe with coefficients in A. The Artin function, denoted β, is a numerical function defined as follows: if t = (t1, . . . , tN), then for all integer i and for all F(t) = (F1(t), . . . ,Fe(t)) in Ae , β(i) is the smallest integer which verifies the following : if for all j, fj(F(t)) is in (t)β(i)+1, where (t) is the maximal ideal in A, then there exists G(t) = (G1(t), . . . ,Ge(t)) in Ae such that fj(G(t)) = 0 for all 0
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Submitted on : Monday, December 6, 2010 - 3:20:54 PM
Last modification on : Monday, March 9, 2020 - 6:15:54 PM
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• HAL Id : tel-00543687, version 1

### Citation

Sahar Saleh. Calcul de la fonction d'Artin d'une singularité plane. Mathématiques [math]. Université d'Angers, 2010. Français. ⟨tel-00543687⟩

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