Quantum projective planes as certain graded twisted tensor products

Let K be an algebraically closed field. Building upon previous work, we classify, up to isomorphism of graded algebras, quadratic graded twisted tensor products of K[x, y] and K[z]. When such an algebra is ArtinSchelter regular, we identify its point scheme and type, in the sense of [5]. We also describe which three-dimensional Sklyanin algebras contain a subalgebra isomorphic to a quantum P, and we show that every algebra in this family is a graded twisted tensor product of K −1[x, y] and K[z].