Abstract :
The homogeneous coordinate ring of a quantum projective plane is a 3-dimensional Artin–Schelter regular algebra with the same Hilbert series as the polynomial ring in three variables; such an algebraAis a graded noncommutative analogue of the polynomial ring in three variables. WhenAis a finite module over its centerZ(A), we define the schemeS = Proj(Z(A)) and the sheaf of S-algebras by (S(f)) = A[f − 1]0. The center of is defined by (S(f)) = Z(A[f − 1]0) and following Grothendieck we may define the scheme Spec( ). The algebrasAfall into several families, and for many of these it has been shown that Spec( ) 2whenAis finite over its center. This paper shows that Spec( ) 2for two more families.
