On the number of generators of ideals defining Gorenstein Artin algebras with Hilbert function (Formula Presented)

Abstract

Let (Formula presented.) be a graded Gorenstein Artin algebra. (Formula presented.) for some (Formula presented.) in the divided power algebra (Formula presented.). Suppose that (Formula presented.) is a height one ideal generated by (Formula presented.) quadrics so that (Formula presented.) after a possible change of variables. Let (Formula presented.). Then (Formula presented.) and (Formula presented.) is said to be (Formula presented.) -generic if (Formula presented.). In this article we prove necessary conditions, in terms of (Formula presented.) , for an ideal to be (Formula presented.) -generic. With some extra assumptions on the exponents of terms of (Formula presented.) , we obtain a characterization for height four ideals (Formula presented.) to be (Formula presented.) -generic. © 2014, The Managing Editors.