The homogeneous coordinate ring of the quantum projective plane

Abstract

We define holomorphic structures on canonical line bundles on the quantum projective plane. The space of holomorphic sections of these line bundles will determine the quantum homogeneous coordinate ring of $\qp^2_q$. We also show that the holomorphic structure of $\qp^2_q$ is naturally represented by a twisted positive Hochschild 4-cocycle.