Let $\pi:X=\mathbb{P}_n\smallsetminus p\rightarrow \mathbb{P}_{n-1}$ be the linear projection. What is the cokernel of the morphism $$ 0\rightarrow \mathcal{O}_{\mathbb{P}_{n-1}}\rightarrow \pi_*(\mathcal{O}_X)? $$
1 Answer
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$X$ is the total space of line bundle $O(1)$ on $P^{n-1}$. Consequently, $$ \pi_*(O_X) = O \oplus O(-1) \oplus O(-2) \oplus \dots $$ and the cokernel is $\oplus_{i\ge 1} O(-i)$.