Gotzmann ideals of the polynomial ring

Satoshi Murai, Takayuki Hibi

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

Let A = K[x 1,..., x n] denote the polynomial ring in n variables over a field K. We will classify all the Gotzmann ideals of A with at most n generators. In addition, we will study Hilbert functions H for which all homogeneous ideals of A with the Hilbert function H have the same graded Betti numbers. These Hilbert functions will be called inflexible Hilbert functions. We introduce the notion of segmentwise critical Hilbert functions and show that segmentwise critical Hilbert functions are inflexible.

Original languageEnglish
Pages (from-to)629-646
Number of pages18
JournalMathematische Zeitschrift
Volume260
Issue number3
DOIs
Publication statusPublished - 2008 Nov 1
Externally publishedYes

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Hilbert Function
Polynomial ring
Graded Betti numbers
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ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Gotzmann ideals of the polynomial ring. / Murai, Satoshi; Hibi, Takayuki.

In: Mathematische Zeitschrift, Vol. 260, No. 3, 01.11.2008, p. 629-646.

Research output: Contribution to journalArticle

Murai, Satoshi ; Hibi, Takayuki. / Gotzmann ideals of the polynomial ring. In: Mathematische Zeitschrift. 2008 ; Vol. 260, No. 3. pp. 629-646.
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