Let $X$ be a smooth, projective surface in $\mathbb{P}^3$ and $p \subset X$ a closed point in $X$. How do I compute $H^1(\mathcal{O}\_{X\backslash p})$? 
Any reference/idea will be most welcome.



Sheaf cohomology of a complement of finitely many points
For what follows, I recommend SGA 2 ([available on Arxiv](https://arxiv.org/abs/math/0511279)). There is an exact sequence
$$0\rightarrow H^1(X,\mathcal{O}\_X)\rightarrow H^1(X\smallsetminus p,\mathcal{O}\_X)\rightarrow H^2\_{p}(X,\mathcal{O}\_X)\rightarrow H^2(X,\mathcal{O}\_X)$$
where $ H^2\_{p}(X,\mathcal{O}\_X)$ is infinite-dimensional, while $H^i(X,\mathcal{O}\_X)$ is finite-dimensional. Therefore $H^1(X\smallsetminus p,\mathcal{O}\_X)$ is infinite-dimensional. The computation of $ H^2\_{p}(X,\mathcal{O}\_X)$ given in SGA 2 and the exact sequence above give an expression for this space, probably not very pleasant. 


