Fonction asymptotique de Samuel des sections hyperplanes et multiplicité

2009/01/12 by Hickel, Michel
#13B22 (Primary) 13C15 #13F25 (Secondary) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.0901.1653

Abstract

Let (A,\mathfrakm_A,k) be a local noetherian ring and I an \mathfrakm_A-primary ideal. The asymptotic Samuel function (with respect to I) v_I : A\longrightarrow ℝ∪ +∞ is defined by v_I(x)=lim_{k → \+infty}(ord_I(x^k)/(k), ∀ x ∈ A. Similary, one defines for another ideal J, v_I(J) as the minimum of v_I(x) as x varies in J. Of special interest is the rational number v_I(\mathfrakm_A). We study the behavior of the Asymptotic Samuel Function (with respect to I) when passing to hyperplanes sections of A as one does for the theory of mixed multiplicities.

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