The depth of an ideal with a given hilbert function

Satoshi Murai*, Takayuki Hibi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)


Let A = K[x1,⋯,xn] denote the polynomial ring in n variables over a field K with each deg X1 = 1. Let I be a homogeneous ideal of A with I ≠ A and Ha/i the Hilbert function of the quotient algebra A/I .Given a numerical function H : ℕ → ℕ satisfying H = Ha/i for some homogeneous ideal I of A,we write A h for the set of those integers 0 ≤ r ≤ n such that there exists a homogeneous ideal I of A with Ha/i = H and with depth A/I = r. It will be proved that one has either Ah = {0,1,⋯,b} for some 0 ≤ b ≤ n or A|H | = 1.

Original languageEnglish
Pages (from-to)1533-1538
Number of pages6
JournalProceedings of the American Mathematical Society
Issue number5
Publication statusPublished - 2008 May
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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