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# Mathematical Research Letters

## Volume 15 (2008)

### Number 2

### A characterization of Gorenstein Hilbert functions in codimension four with small initial degree

Pages: 331 – 349

DOI: http://dx.doi.org/10.4310/MRL.2008.v15.n2.a11

#### Authors

#### Abstract

The main goal of this paper is to characterize the Hilbert functions of all (artinian) codimension 4 Gorenstein algebras that have at least two independent relations of degree four. This includes all codimension 4 Gorenstein algebras whose initial relation is of degree at most 3. Our result shows that those Hilbert functions are exactly the so-called {\em SI-sequences} starting with $(1,4,h_2,h_3,...)$, where $h_4 \leq 33$. In particular, these Hilbert functions are all unimodal. We also establish a more general unimodality result, which relies on the values of the Hilbert function not being too big, but is independent of the initial degree.