On the number of generators of ideals defining Gorenstein Artin algebras with Hilbert function (1,n+1, 1+n+1\choose 2,...,n+1\choose 2+1, n+1,1)

2013/04/01 by Sabine El Khoury, Khoury, Sabine El, A. V. Jayanthan +3
Mathematics · #13C05 #13H10 #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #msc:13C05 #msc:13H10

paper · pdf · doi:10.48550/arxiv.1304.0305

Third author's email address was incorrect in the first version. It has been corrected now

arxiv created 2013/04/03 · arxiv updated 2013/04/04

Abstract

Let R = k[w, x₁,..., x_n]/I be a graded Gorenstein Artin algebra . Then I = \ann F for some F in the divided power algebra k_DP[W, X₁,..., X_n]. If RI₂ is a height one idealgenerated by n quadrics, then I₂ ⊂ (w) after a possible change of variables. Let J = I ∩ k[x₁,..., x_n]. Then μ(I) ≤ μ(J)+n+1 and I is said to be generic if μ(I) = μ(J) + 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.

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