On the stability of regular algebras

Abstract

We characterize which quadratic regular algebras of global dimension 3 are stable in the sense of Behrend-Noohi. (This notion of stability is a non-commutative analogue of Hilbert stability.) We describe the quasi-projective stack of stable quadratic regular algebras of dimension 3. This provides the first non-trivial, non-commutative examples of stability a la Behrend-Noohi.