# On the number of generators of ideals defining Gorenstein Artin algebras with Hilbert function \$ 1,n 1, 1 {n 1choose 2},...,{n 1choose 2} 1, n 1,1\$

On the number of generators of ideals defining Gorenstein Artin algebras with Hilbert function \$ 1,n 1, 1 {n 1choose 2},...,{n 1choose 2} 1, n 1,1\$ - Download this document for free, or read online. Document in PDF available to download.

Download or read this book online for free in PDF: On the number of generators of ideals defining Gorenstein Artin algebras with Hilbert function \$ 1,n 1, 1 {n 1choose 2},

.,{n 1choose 2} 1, n 1,1\$

Let \$R = kw, x 1,

., x n-I\$ be a graded Gorenstein Artin algebra . Then \$I = \ann F\$ for some \$F\$ in the divided power algebra \$k {DP}W, X 1,

., X n\$. If \$RI 2\$ is a height one idealgenerated by \$n\$ quadrics, then \$I 2 \subset w\$ after a possible change of variables. Let \$J = I \cap kx 1,

., x n\$. Then \$\muI \le \muJ+n+1\$ and \$I\$ is said to be generic if \$\muI = \muJ + n+1\$. In this article we prove necessary conditions, in terms of \$F\$, for an ideal to be generic. With some extra assumptions on the exponents of terms of \$F\$, we obtain a characterization for \$I = \ann F\$ to be generic in codimension four.

Author: Sabine El Khoury; A. V. Jayanthan; Hema Srinivasan

Source: https://archive.org/