Smooth points of \(\text{Gor}(T)\)
Let \(R\) be an artinian Gorenstein algebra that is a graded quotient of \(k[x_0, x_1, \dots, x_n]\) (where \(k\) is an algebraically closed field of characteristic 0). \textit{Iarrobino} and \textit{Kanev} [``The length of a homogeneous form, determinantal loci of catalecticants and Gorenstein algebras'' (preprint)] have introduced the classifying spaces \(\text{Gor} (T)\) and \({\mathcal G}\)\textit{or}\((T)\) for \(R\) where \(T\) is a symmetric sequence. This paper deals with some of the problems concerning the dimension and smoothness of these spaces for the case \(n=3\), i.e., for artinian Gorenstein algebras of embedding dimension \(\leq 3\). A number of examples and results are given and some conjectures are made which are verified in several cases.
scientific article; zbMATH DE number 1097605
scientific article