Abstract
We define holomorphic structures on canonical line bundles of the quantum projective space C P q ℓ and identify their space of holomorphic sections. This determines the quantum homogeneous coordinate ring of the quantum projective space. We show that the fundamental class of C P q ℓ is naturally presented by a twisted positive Hochschild cocycle. Finally, we verify the main statements of the Riemann–Roch formula and the Serre duality for C P q 1 and C P q 2 .
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