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 -