The depth of an ideal with a given Hilbert function
Authors:
Satoshi Murai and Takayuki Hibi
Journal:
Proc. Amer. Math. Soc. 136 (2008), 15331538
MSC (2000):
Primary 13C15; Secondary 13D40
Published electronically:
January 17, 2008
MathSciNet review:
2373580
Fulltext PDF Free Access
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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, 5600043, Japan
Email:
smurai@ist.osakau.ac.jp
Takayuki Hibi
Affiliation:
Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, Toyonaka, Osaka, 5600043, Japan
Email:
hibi@math.sci.osakau.ac.jp
DOI:
http://dx.doi.org/10.1090/S0002993908090679
PII:
S 00029939(08)090679
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.
