The depth of an ideal with a given Hilbert function

Authors:
Satoshi Murai and Takayuki Hibi

Journal:
Proc. Amer. Math. Soc. **136** (2008), 1533-1538

MSC (2000):
Primary 13C15; Secondary 13D40

DOI:
https://doi.org/10.1090/S0002-9939-08-09067-9

Published electronically:
January 17, 2008

MathSciNet review:
2373580

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Abstract: Let denote the polynomial ring in variables over a field with each . Let be a homogeneous ideal of with and the Hilbert function of the quotient algebra . Given a numerical function satisfying for some homogeneous ideal of , we write for the set of those integers such that there exists a homogeneous ideal of with and with . It will be proved that one has either for some or .

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Additional Information

**Satoshi Murai**

Affiliation:
Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, Toyonaka, Osaka, 560-0043, Japan

Email:
s-murai@ist.osaka-u.ac.jp

**Takayuki Hibi**

Affiliation:
Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, Toyonaka, Osaka, 560-0043, Japan

Email:
hibi@math.sci.osaka-u.ac.jp

DOI:
https://doi.org/10.1090/S0002-9939-08-09067-9

Keywords:
Hilbert functions,
depth,
lexsegment ideals

Received by editor(s):
August 9, 2006

Received by editor(s) in revised form:
December 5, 2006

Published electronically:
January 17, 2008

Additional Notes:
The first author is supported by JSPS Research Fellowships for Young Scientists

Communicated by:
Bernd Ulrich

Article copyright:
© Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.