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Jun 22, 2020 at 20:30 comment added Piotr Achinger For $X$ normal the connected component of ${\rm Pic}_X$ is projective (and over $\mathbf{C}$ it is an abelian variety). This was proved by Grothendieck in FGA, see Kleiman's survey article "The Picard scheme".
Jun 22, 2020 at 17:28 history asked user45397 CC BY-SA 4.0