Illinois Journal of Mathematics

Ideals attaining a given Hilbert function

Matthew J. Rodriguez

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Abstract

We improve the result of Charalambous and Evans [C-E] to show that the Betti number sequence in their example of incomparable minimals among the resolutions for a fixed Hilbert function is indeed minimal. Their example was dependent upon the graded betti numbers. We give an example of a finite length Hilbert function and two cyclic finite length modules attaining the Hilbert function for which the betti number sequences are incomparable, i.e., independent of the grading.

Article information

Source
Illinois J. Math., Volume 44, Issue 4 (2000), 821-827.

Dates
First available in Project Euclid: 19 October 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1255984693

Digital Object Identifier
doi:10.1215/ijm/1255984693

Mathematical Reviews number (MathSciNet)
MR1804318

Zentralblatt MATH identifier
0973.18008

Subjects
Primary: 13D40: Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series
Secondary: 13D02: Syzygies, resolutions, complexes

Citation

Rodriguez, Matthew J. Ideals attaining a given Hilbert function. Illinois J. Math. 44 (2000), no. 4, 821--827. doi:10.1215/ijm/1255984693. https://projecteuclid.org/euclid.ijm/1255984693


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