Let （R, m） be a Cohen-Macaulay local ring of dimension d, I an mprimary ideal and K an ideal containing I. Assuming that I has minimal （almost minimal） mixed multiplicity with respect to K, we get some results on ...Let （R, m） be a Cohen-Macaulay local ring of dimension d, I an mprimary ideal and K an ideal containing I. Assuming that I has minimal （almost minimal） mixed multiplicity with respect to K, we get some results on the Hilbert coefficients of fiber cones.展开更多
Let F be a Hilbert filtration with respect to a Cohen-Macaulay module M. When G（F, M） and FK（F,M） have almost maximal depths, the Hilbert coefficients gi（F, M） is calculated. In the general case, an upper bound ...Let F be a Hilbert filtration with respect to a Cohen-Macaulay module M. When G（F, M） and FK（F,M） have almost maximal depths, the Hilbert coefficients gi（F, M） is calculated. In the general case, an upper bound for g2（F, M） is also given.展开更多
Let F be a Hilbert filtration with respect to a Cohen-Macaulay R-module M. When G(F,M) and FK(F,M) have almost maximal depths, we show that the length λ(KInM/KJIn-1M) and the reduction number rJK (F,M) are independen...Let F be a Hilbert filtration with respect to a Cohen-Macaulay R-module M. When G(F,M) and FK(F,M) have almost maximal depths, we show that the length λ(KInM/KJIn-1M) and the reduction number rJK (F,M) are independent of J. Lower bounds for the first and second Hilbert coefficients are obtained.展开更多
Let S = K[x1,... ,xn] be the polynomial ring over a field K, and let I C S be a graded ideal. It is shown that the higher iterated Hilbert coefficients of the graded S-modules Tori^S（M,Ik） and Exts^i（M,Ik） are pol...Let S = K[x1,... ,xn] be the polynomial ring over a field K, and let I C S be a graded ideal. It is shown that the higher iterated Hilbert coefficients of the graded S-modules Tori^S（M,Ik） and Exts^i（M,Ik） are polynomial functions in k, and an upper bound for their degree is given. These results are derived by considering suitable bigraded modules.展开更多
文摘Let （R, m） be a Cohen-Macaulay local ring of dimension d, I an mprimary ideal and K an ideal containing I. Assuming that I has minimal （almost minimal） mixed multiplicity with respect to K, we get some results on the Hilbert coefficients of fiber cones.
基金the National Natural-Science Foundation of China(No.10371085).
文摘Let F be a Hilbert filtration with respect to a Cohen-Macaulay module M. When G（F, M） and FK（F,M） have almost maximal depths, the Hilbert coefficients gi（F, M） is calculated. In the general case, an upper bound for g2（F, M） is also given.
基金the National Natural Science Foundation of China (No.10771152)
文摘Let F be a Hilbert filtration with respect to a Cohen-Macaulay R-module M. When G(F,M) and FK(F,M) have almost maximal depths, we show that the length λ(KInM/KJIn-1M) and the reduction number rJK (F,M) are independent of J. Lower bounds for the first and second Hilbert coefficients are obtained.
文摘Let S = K[x1,... ,xn] be the polynomial ring over a field K, and let I C S be a graded ideal. It is shown that the higher iterated Hilbert coefficients of the graded S-modules Tori^S（M,Ik） and Exts^i（M,Ik） are polynomial functions in k, and an upper bound for their degree is given. These results are derived by considering suitable bigraded modules.
