  We define holomorphic structures on canonical line bundles of the quantum
projective space $\qp^{\ell}_q$ 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 $\qp^{\ell}_q$
is naturally presented by a twisted positive Hochschild cocycle. Finally, we
verify the main statements of Riemann-Roch formula and Serre duality for
$\qp^{1}_q$ and $\qp^{2}_q$.
