On the Multiplicity of Rees Algebras of Good Filtrations

Abstract

Abstract. Let (A, m) be a Noetherian local ring. Let F = {I n } n≥0 be a good filtration of ideals in A. Denote by R(F ) = n≥0 I n t n 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.