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2012•Kyushu Journal of MathematicsOpen access

ON THE MULTIPLICITY OF REES ALGEBRAS OF GOOD FILTRATIONS

Duong Quôc Việt, Le Van DINH

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Abstract

Let (A, m) be a Noetherian local ring. Let F ={In}n≥0 be a good filtration of ideals in A. Denote by R(F) = ⊕n≥0 Intn the Rees algebra of F. In this paper we investigate the mixed multiplicities of F and the relationship between the multiplicity of R(F) and the mixed multiplicities of F. As an application, we obtain several multiplicity formulas that express the multiplicity of R(F) as a sum of Hilbert-Samuel multiplicities of some quotient rings of A.

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Let (A, m) be a Noetherian local ring. Let F ={In}n≥0 be a good filtration of ideals in A. Denote by R(F) = ⊕n≥0 Intn the Rees algebra of F. In this paper we investigate the mixed multiplicities of F and the relationship between the multiplicity of R(F) and the mixed multiplicities of F. As an application, we obtain several multiplicity formulas that express the multiplicity of R(F) as a sum of Hilbert-Samuel multiplicities of some quotient rings of A.

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Available abstract

Let (A, m) be a Noetherian local ring. Let F ={In}n≥0 be a good filtration of ideals in A. Denote by R(F) = ⊕n≥0 Intn the Rees algebra of F. In this paper we investigate the mixed multiplicities of F and the relationship between the multiplicity of R(F) and the mixed multiplicities of F. As an application, we obtain several multiplicity formulas that express the multiplicity of R(F) as a sum of Hilbert-Samuel multiplicities of some quotient rings of A.

Key concepts: Multiplicity (mathematics), Mathematics, Noetherian, Quotient, Local ring, Pure mathematics, Graded ring, Combinatorics

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