A Characterization of Gorenstein Hilbert Functions in Codimension Four with Small Initial Degree

@inproceedings{Migliore2008ACO,
  title={A Characterization of Gorenstein Hilbert Functions in Codimension Four with Small Initial Degree},
  author={Juan Migliore and Uwe Nagel and Fabrizio Zanello},
  year={2008}
}
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 SI-sequences starting with (1, 4, h2, h3, ...), where h4 ≤ 33. In particular, these Hilbert functions are all unimodal. We also establish a more… CONTINUE READING