Growth of multiplicities of graded families of ideals

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• 作者：Huy Tà ; i Hà ; ^a ; ¹ ; ^{tha@tulane.edu" class="auth_mail" title="E-mail the corresponding author} ; Pham An Vinh^b ; ^{vapnnc@mizzou.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：13H15 ; 13H05 ; 14B05 ; 14C20
• 刊名：Journal of Algebra
• 出版年：2016
• 出版时间：15 April 2016
• 年：2016
• 卷：452
• 期：Complete
• 页码：311-323
• 全文大小：332 K

文摘

Let (R,m)$(R,\mathfrak{m})$ be a Noetherian local ring of dimension d>0$d>0$. Let I_•={I_n}_n∈N$I_{•}={\{I_n\}}_{n\in \mathbb{N}}$ be a graded family of m$\mathfrak{m}$-primary ideals in R  . We examine how far off from a polynomial can the length function ℓ_R(R/I_n)${\ell }_R(R/I_n)$ be asymptotically. More specifically, we show that there exists a constant γ>0$\gamma >0$ such that for all n≥0$n\ge 0$,