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

Abstract

Let A be a Noetherian local ring with the maximal ideal m and an m-primary ideal J. Let S = {N-ary circled plus operator}n ≥ 0 Sn be a finitely generated standard graded algebra over A. Set S+ = {N-ary circled plus operator}n > 0 Sn. Denote by FJ (S) = {N-ary circled plus operator}n ≥ 0 → (Sn / J Sn) the fiber cone of S with respect to J. The paper characterizes the multiplicity and the Cohen-Macaulayness of FJ (S) in terms of minimal reductions of S+. © 2009 Elsevier B.V. All rights reserved.