A complex-analytic proof of a criterion for isomorphism of Artinian Gorenstein algebras (Q289637)

The author gives a new proof of a criterion for the isomorphism of two Artinian Gorenstein algebras over fields \(\mathbb{R}\) and \(\mathbb{C}\). The criterion is expressed in terms of some hypersurfaces associated to these algebras. The novelty is a complex-analytic proof of the criterion. As an application of the criterion, he establishes which of the following algebras \(A_{t}:=k[x,y]/(2x^{3}+txy^{3},tx^{2}y^{2}+2y^{5}), \) \(t\neq \pm 2,\) are isomorphic (the answer \(A_{t}\cong A_{t^{\prime }}\) iff \(t=\pm t^{\prime }).\)