Multiplicity and Cohen-Macaulayness of Fiber Cones of Good Filtrations

Abstract

Abstract. Let A be a Noetherian local ring with the maximal ideal m and an m-primary ideal J . Let F = {I n } n≥0 be a good filtration of ideals in A. Denote by F J (F ) = n≥0 (I n /JI n )t n the fiber cone of F with respect to J. In this paper we characterize the multiplicity and the Cohen-Macaulayness of F J (F ) in terms of minimal reductions of F .

On the Multiplicity of Rees Algebras of Good Filtrations

“…Basic facts about weak-(FC)-sequences of good filtrations were pointed out in [16]. In the following we also give some properties of these sequences.…”

“…In this section we develop the method of Viet in [12] to interpret mixed multiplicities of a good filtration as the Hilbert-Samuel multiplicity. We recall here the concept of (FC)-sequences of good filtrations that were introduced in [16]. This is a kind of variant of superficial sequences.…”

“…The existence of weak-(FC)-sequences of good filtrations was shown in [16]. Basic facts about weak-(FC)-sequences of good filtrations were pointed out in [16].…”