### 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 |
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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

*Mathematische Zeitschrift*,

*260*(3), 629-646. https://doi.org/10.1007/s00209-007-0293-2

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

Research output: Contribution to journal › Article

*Mathematische Zeitschrift*, vol. 260, no. 3, pp. 629-646. https://doi.org/10.1007/s00209-007-0293-2

}

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 -