Abstract: We consider a natural holomorphic structure on the quantum projective space $\mathbb{C}P^l_q$ already presented in the literature and define holomorphic structures on canonical quantum line bundles on it. The space of holomorphic sections of these line bundles then will determine the quantum homogeneous coordinate ring of $\mathbb{C}P^l_q$. We define bimodule connections on canonical line bundles and this enables us to identify the quantum homogeneous coordinate ring of $\mathbb{C}P^l_q$ with the ring of twisted polynomials. We also introduce a twisted positive Hochschild $2l$-cocycle on $\mathbb{C}P^l_q$, by using the complex structure of $\mathbb{C}P^l_q$, and show that it is cohomologous to its fundamental class which is represented by a twisted cyclic cocycle. This certainly provides further evidence for the belief that holomorphic structures in noncommutative geometry should be represented by (extremal) positive Hochschild cocycles within the fundamental class. Finally we verify directly that the main statements of the Riemann-Roch formula and Serre duality theorem hold for $\mathbb{C}P^1_q$ and $\mathbb{C}P^2_q$. This is joint work with Masoud Khalkhali.