Let $\pi:\mathbb{C}^{n}\setminus{O}\rightarrow\mathbb{CP}^{n-1}, n\geq 3$ be the projection from affine space without the origin to the projective space. If we pull back the tangent bundle of $\mathbb{CP}^{n-1}$ we would get a nontrivial bundle over $\mathbb{C}^{n}\setminus{O}$. Now my question would be: what is $H^{1}(\mathbb{C}^{n}\setminus{O},\pi^{*}\mathcal{T}_{\mathbb{CP}^{n-1}})$?
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Fixed a typo in the dimension of porjective space and clarified the definition of
SashaP
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Bundle over $\mathbb{C}^{n}\setminus{O}$
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