On parameter spaces for artin level algebras

Abstract

The set of all artin level quotients of a polynomial algebra in n variables having specified socle degree and type admits a parameter space. It is in fact a quasiprojective variety, naturally embedded in a Grassmannian. We give a geometric description of this variety in the case of two variables. Then we give some sufficient conditions for the parameter variety to be projectively normal in the Plucker embedding.