Classes of Graded Ideals with Given Data in the Exterior Algebra

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).