Geometric classification of quadratic algebras in two variables

Abstract

In this paper, we classify quadratic algebras in two variables at two levels: (1) up to isomorphism of graded algebras, (2) up to graded Morita equivalence. In general, it is difficult to classify algebras by looking at generators and relations, so we take a geometric approach, namely, using point schemes defined by Artin, Tate and Van den Bergh, to complete the classification.