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Feb 5, 2011 at 5:36 comment added Torsten Ekedahl I think it is factorial: The Picard group of the real projective quadric $x^2-y^2-z^2-t^2$ is generated by hyperplane sections and $x^2-y^2-z^2-1$ is a complement of a hyperplane and thus the whole Picard group is killed off.
Feb 4, 2011 at 20:44 comment added Hugh Thomas Sorry, since this doesn't answer the question as posed, maybe I should have left it as a comment.
Feb 4, 2011 at 20:38 history answered Hugh Thomas CC BY-SA 2.5