Let （R,m） be a Cohen-Macaulay local ring of dimension d with infinite residue field, I an m-primary ideal and K an ideal containing I. Let J be a minimal reduction of I such that, for some positive integer k, KIn ∩...Let （R,m） be a Cohen-Macaulay local ring of dimension d with infinite residue field, I an m-primary ideal and K an ideal containing I. Let J be a minimal reduction of I such that, for some positive integer k, KIn ∩ J = JKIn-1 for n ≤ k ？ 1 and λ（ JKKIIkk-1 ） = 1. We show that if depth G（I） ≥ d-2, then such fiber cones have almost maximal depth. We also compute, in this case, the Hilbert series of FK（I） assuming that depth G（I） ≥ d - 1.展开更多
In this paper, we introduce the concept of the spanning simplicial complex As（G） associated to a simple finite connected graph G. We characterize all spanning trees of the uni-cyclic graph Un,m. In particular, we gi...In this paper, we introduce the concept of the spanning simplicial complex As（G） associated to a simple finite connected graph G. We characterize all spanning trees of the uni-cyclic graph Un,m. In particular, we give a formula for computing the Hilbert series and h-vector of the Stanley-Reisner ring k[△s（Un,m）]. Finally, we prove that the spanning simplicial complex △s（Un,m） is shifted and hence is shellable.展开更多
In this paper, for the highest weight module V4 of sl（2,C） with the highest weight 4, we describe subalgebras Sβ（V4）＋ and Sγ（V4）＋ of the βγ-system coset S（V4）＋ by giving their generators. These eoset su...In this paper, for the highest weight module V4 of sl（2,C） with the highest weight 4, we describe subalgebras Sβ（V4）＋ and Sγ（V4）＋ of the βγ-system coset S（V4）＋ by giving their generators. These eoset subalgebras are interesting, new examples of strongly finitely generated vertex algebra.展开更多
We introduce first the spanning simplicial complex(SSC)of a multigraph g,which gives a generalization of the SSC associated with a simple graph G.Combinatorial properties are discussed for the SSC of a family of uni-c...We introduce first the spanning simplicial complex(SSC)of a multigraph g,which gives a generalization of the SSC associated with a simple graph G.Combinatorial properties are discussed for the SSC of a family of uni-cyclic multigraphs U_(n)^(r),m with n edges including r multiple edges within and outside the cycle of length m,which are then used to compute the f-vector and Hilbert series of face ring k[△s(U_(n)^(r),m)]for the SSC △s(U_(n)^(r),m)(un,m).Moreover,we find the associated primes of the facet ideal I_(F)(△s(U_(n)^(r),m).Finally,we device a formula for homology groups of △s(U_(n)^(r),m) prove that the SsC of a family of uni-cyclic multigraphs is Cohen-Macaulay.展开更多
基金Supported by the National Natural Science Foundation of China (Grant No.10771152)
文摘Let （R,m） be a Cohen-Macaulay local ring of dimension d with infinite residue field, I an m-primary ideal and K an ideal containing I. Let J be a minimal reduction of I such that, for some positive integer k, KIn ∩ J = JKIn-1 for n ≤ k ？ 1 and λ（ JKKIIkk-1 ） = 1. We show that if depth G（I） ≥ d-2, then such fiber cones have almost maximal depth. We also compute, in this case, the Hilbert series of FK（I） assuming that depth G（I） ≥ d - 1.
文摘In this paper, we introduce the concept of the spanning simplicial complex As（G） associated to a simple finite connected graph G. We characterize all spanning trees of the uni-cyclic graph Un,m. In particular, we give a formula for computing the Hilbert series and h-vector of the Stanley-Reisner ring k[△s（Un,m）]. Finally, we prove that the spanning simplicial complex △s（Un,m） is shifted and hence is shellable.
基金Supported by National Natural Science Foundation of China (10971071)Provincial Foundation of Innovative Scholars of Henan
文摘In this paper, for the highest weight module V4 of sl（2,C） with the highest weight 4, we describe subalgebras Sβ（V4）＋ and Sγ（V4）＋ of the βγ-system coset S（V4）＋ by giving their generators. These eoset subalgebras are interesting, new examples of strongly finitely generated vertex algebra.
文摘We introduce first the spanning simplicial complex(SSC)of a multigraph g,which gives a generalization of the SSC associated with a simple graph G.Combinatorial properties are discussed for the SSC of a family of uni-cyclic multigraphs U_(n)^(r),m with n edges including r multiple edges within and outside the cycle of length m,which are then used to compute the f-vector and Hilbert series of face ring k[△s(U_(n)^(r),m)]for the SSC △s(U_(n)^(r),m)(un,m).Moreover,we find the associated primes of the facet ideal I_(F)(△s(U_(n)^(r),m).Finally,we device a formula for homology groups of △s(U_(n)^(r),m) prove that the SsC of a family of uni-cyclic multigraphs is Cohen-Macaulay.
