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.

Revised version which supplies a missing attribution. To appear in Mich. Math. J