The concept of multi-Rees algebras is e.g. connected with mixed multiplicities (cf. [Te] and [HHRTa]) and joint reductions (cf. [Re]). Verma studied for instance the Cohen-Macaulayness of multi-Rees algebras of ideals having joint reduction number zero (see [Ve]). He considered multi-Rees algebras with respect to different ideals I_1,...,I_r of A, i.e. A-algebras of the form: A[I_1t_1, I_2t_2, ... ,I_rt_r], but only in the case that dim A = 2 (plus some additional assumptions). A result on the Cohen-Macaulayness of multi-Rees algebras of m-primary ideals in a local ring A of dimension two having joint reduction number zero can also be found in [HHRTa]. From a totally different viewpoint, Goto and Nishida studied the Cohen-Macaulay and Gorenstein property of R_A(I_2) in their work on Rees algebras defined by a filtration ([GN]).
展开▼
