MULTIPLICITY AND COHEN-MACAULAYNESS OF FIBER CONES OF GOOD FILTRATIONS

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)tⁿ 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.