Let(A,m)be a Noetherian local ring with maximal ideal m,I an ideal of A,J an m-primary ideal of A,N a finitely generated A-module,S=■n≥0 Sn a finitely generated standard graded algebra over A and M=■n≥0 Mn a finit...Let(A,m)be a Noetherian local ring with maximal ideal m,I an ideal of A,J an m-primary ideal of A,N a finitely generated A-module,S=■n≥0 Sn a finitely generated standard graded algebra over A and M=■n≥0 Mn a finitely generated graded S-module.We characterize the multiplicity and the Cohen-Macaulayness of the fiber cone F(M)=■n≥0 Mn/JM_(n).As an application,we obtain some results on the multiplicity and the Cohen--Macaulayness of the fiber cone■n≥0 I^(n)N/JI^(n)N.展开更多
文摘Let(A,m)be a Noetherian local ring with maximal ideal m,I an ideal of A,J an m-primary ideal of A,N a finitely generated A-module,S=■n≥0 Sn a finitely generated standard graded algebra over A and M=■n≥0 Mn a finitely generated graded S-module.We characterize the multiplicity and the Cohen-Macaulayness of the fiber cone F(M)=■n≥0 Mn/JM_(n).As an application,we obtain some results on the multiplicity and the Cohen--Macaulayness of the fiber cone■n≥0 I^(n)N/JI^(n)N.
