TY - JOUR
T1 - Gotzmann ideals of the polynomial ring
AU - Murai, Satoshi
AU - Hibi, Takayuki
N1 - Funding Information:
The first author is supported by JSPS Research Fellowships for Young Scientists.
PY - 2008/11
Y1 - 2008/11
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.
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U2 - 10.1007/s00209-007-0293-2
DO - 10.1007/s00209-007-0293-2
M3 - Article
AN - SCOPUS:50249161959
SN - 0025-5874
VL - 260
SP - 629
EP - 646
JO - Mathematische Zeitschrift
JF - Mathematische Zeitschrift
IS - 3
ER -