The depth of an ideal with a given Hilbert function期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

The depth of an ideal with a given Hilbert function

Authors:	Satoshi Murai Takayuki Hibi

Affiliation:	Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, Toyonaka, Osaka, 560-0043, Japan ; Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, Toyonaka, Osaka, 560-0043, Japan

Abstract:	Let denote the polynomial ring in variables over a field with each $operatorname{deg} x_i = 1$ . Let be a homogeneous ideal of with and $H_{A/I}$ the Hilbert function of the quotient algebra . Given a numerical function satisfying $H=H_{A/I}$ for some homogeneous ideal of , we write $mathcal{A} _H$ for the set of those integers such that there exists a homogeneous ideal of with $H_{A/I} = H$ and with . It will be proved that one has either $mathcal{A}_H = { 0, 1, ldots, b }$ for some or $vert{mathcal{A}}_Hvert = 1$ .

Keywords:	Hilbert functions depth lexsegment ideals

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