Isomorphism Classes of Certain Artinian Gorenstein Algebras

Abstract

In this paper we attack the problem of the classification, up to analytic isomorphism, of Artinian Gorenstein local k-algebras with a given Hilbert Function. We solve the problem in the case the square of the maximal ideal is minimally generated by two elements and the socle degree is high enough.

On the Gorenstein locus of some punctual Hilbert schemes

“…We obtain the same results proved in [23] and [24] under the restrictive hypothesis char(k) = 0. Finally, in Section 4, we will examine the remaining case, namely…”

“…Kleppe for some interesting and helpful suggestions. A particular thank goes to J. Elias and G. Valla, who pointed out an incongruence in the results proved in Section 3.2 with respect to the more general classification of almost stretched local, Artinian, Gorenstein k-algebras described in [23] and [24].…”

On the irreducibility and the singularities of the Gorenstein locus of the punctual Hilbert scheme of degree 10

“…Indeed, in our proofs we make wide use of some results stated only in the 0-characteristic case (see, e.g. [4,[7][8][9]). …”

A family of local rings with rational Poincaré series

“…Instead, if the square of the maximal ideal of an Artinian reduction is minimally generated by two elements, we say that A is almost stretched. See [11], [9], [5] and [6] for papers concerning these notions.…”