Let $X$ be a compact complex manifold and $Y$ a complex sub manifold of codimension $\ge 2$. If $\pi : X_{Y} \mapsto X$ is the blow-up of $X$ along $Y$, do you have any references for this result :
-$Pic(X_{Y}) = \pi^{*}Pic(X) \otimes \mathbb{Z}$? (whithout using "pure" algebraic geometry arguments but only complex geometry).
Here $Pic(X) = H^{1}(X, \mathcal{O}_{X}^{*})$ are all the classes of isomorphism of holomorphic line bundles over $X$.
I thank you in advance and wish you a good day.