The dimension of the determinantal scheme vs (t,t,2) of the catalecticant matrix

Abstract

Let T be a Gorenstein sequence of a graded artinian Gorenstein ring k[x 0,x 1,x 2]/I We develop a dimension formula for PGor(T) in terms of the alignment character. Based on our formula, we find a very large component of Vs (t,t,2) when s=rt-1+1 and t is large enough. This answers Diesel’s conjecture negatively. Further we show that Vs (t,t,2) is irreducible of dimension 3s-1 for s ≤t+1,t ≥ 2 and dim Vs (t,t,2)= 3s-1 for small s. Finally an algorithm to calculate dim Vs (t,t,2) is constructed, and we find the values of dim Vs (t,t,2) for t ≤ 16.