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 | |
| Publication status | Published - 2008 Nov 1 |
| Externally published | Yes |
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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 journal › Article
}
TY - JOUR
T1 - Gotzmann ideals of the polynomial ring
AU - Murai, Satoshi
AU - Hibi, Takayuki
PY - 2008/11/1
Y1 - 2008/11/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=50249161959&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=50249161959&partnerID=8YFLogxK
U2 - 10.1007/s00209-007-0293-2
DO - 10.1007/s00209-007-0293-2
M3 - Article
AN - SCOPUS:50249161959
VL - 260
SP - 629
EP - 646
JO - Mathematische Zeitschrift
JF - Mathematische Zeitschrift
SN - 0025-5874
IS - 3
ER -