Illinois Journal of Mathematics

Ideals attaining a given Hilbert function

Matthew J. Rodriguez

Full-text: Open access


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

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

First available in Project Euclid: 19 October 2009

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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

Export citation