Gotzmann ideals of the polynomial ring

Satoshi Murai; Takayuki Hibi

doi:10.1007/s00209-007-0293-2

Gotzmann ideals of the polynomial ring

Satoshi Murai, Takayuki Hibi

Research output: Contribution to journal › Article

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 language	English
Pages (from-to)	629-646
Number of pages	18
Journal	Mathematische Zeitschrift
Volume	260
Issue number	3
DOIs	https://doi.org/10.1007/s00209-007-0293-2
Publication status	Published - 2008 Nov 1
Externally published	Yes

ASJC Scopus subject areas

Mathematics(all)

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Murai, S., & Hibi, T. (2008). Gotzmann ideals of the polynomial ring. Mathematische Zeitschrift, 260(3), 629-646. https://doi.org/10.1007/s00209-007-0293-2

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