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Polynôme d’Hilbert-Samuel des clôtures intégrales des puissances d’un idéal m-primaire. (French) Zbl 0558.13003
Let R be a normal, finitely generated k-algebra over an algebraically closed field k, m a maximal ideal, Q an m-primary ideal and \(\overline{Q^ n}\) the integral closure of \(Q^ n\). Then L(R/\(\overline{Q^ n})\) is a polynomial, the Hilbert-Samuel polynomial, for n sufficiently large. The coefficients of this polynomial are interpreted geometrically b using the Riemann-Roch theorem of the normal blow-up of Q. Only in the case when Spec R is Cohen-Macaulay with isolated singularities along the exceptional divisor, the coefficients of L(R/\(\overline{Q^ n})\), \(n>>0\), are invariants of successive general hyperplane sections.
Reviewer: R.Fröberg

MSC:
14H20 Singularities of curves, local rings
13H10 Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)
13H15 Multiplicity theory and related topics
13E10 Commutative Artinian rings and modules, finite-dimensional algebras
13A15 Ideals and multiplicative ideal theory in commutative rings
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