On the multiplicity and the Cohen-Macaulayness of fiber cones of graded algebras

Let A be a Noetherian local ring with the maximal ideal m and an m-primary ideal J. Let S=?_n≥0S_n be a finitely generated standard graded algebra over A. Set S⁺=?_n>0S_n. Denote by F_J(S)=?_n≥0→(S_n/JS_n) the fiber cone of S with respect to J. The paper characterizes the multiplicity and the Cohen-Macaulayness of F_J(S) in terms of minimal reductions of S⁺.