Classes of Graded Ideals with Given Data in the Exterior Algebra

Abstract

Let ℱ be the family of graded ideals J in the exterior algebra E of a n-dimensional vector space over a field K such that e(E/J) = dim _K (E/J) = e, indeg(E/J) = i and H _E/J (i) = dim _K (E/J) _i are fixed integers. It is shown that there exists a unique lexsegment graded ideal J(n, e, i) ∊ ℱ whose Betti numbers give an upper bound for the Betti numbers of the ideals of ℱ. The authors continue the computation of upper bounds for the Betti numbers of graded ideals with given data started in Crupi and Utano (1999).

Key Words:

• Exterior algebra
• Hilbert functions

Mathematics Subject Classification:

• Primary 13D02
• Secondary 13D40

Notes

Communicated by W. Bruns.