Blowing up quantum weighted projective planes

Quantum weighted projective planes of degree (1,1,n) were classified by Stephenson. We show that the blowups of some of these spaces are quantum ruled surfaces as defined by Patrick [PhD thesis, MIT, 1997]. This is a quantum version of the fact that projective cones over rational normal curves blowup to rational ruled surfaces. The class of algebras which we can exhibit as blowdowns of quantum ruled surfaces are those which can be twisted to Ore extensions of k[x,y].