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Apr 14, 2014 at 8:15 comment added Piotr Achinger The question asked for a holomorphic, not algebraic, section. In the situation in question, the exponential sequence shows that since $H^1(X, O_X) = H^2(X, O_X) = 0$, we have $Pic(X) = H^2(X, \mathbb{Z})$, which is zero.
Apr 14, 2014 at 8:12 history answered Sasha CC BY-SA 3.0