# The homogeneous coordinate ring of the quantum projective plane - Mathematics > Quantum Algebra

Abstract: We define holomorphic structures on canonical line bundles on the quantumprojective plane. The space of holomorphic sections of these line bundles willdetermine the quantum homogeneous coordinate ring of \$\qp^2 q\$. We also showthat the holomorphic structure of \$\qp^2 q\$ is naturally represented by atwisted positive Hochschild 4-cocycle.