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Oct 6, 2014 at 16:07 vote accept Dubious
Oct 6, 2014 at 16:01 comment added Pete L. Clark Hartshorne, Theorem V.5.7, proves Castelnuovo's Criterion over any algebraically closed field.
Oct 6, 2014 at 13:49 comment added Dubious Beautiful answer but I have still a doubt when you at the end write "...so the contractions can be done over $\overline{\mathbb Q}$". I formally don't see this. Why the contraction of a $(-1)$-curve defined over $\overline {\mathbb Q}$ is a morphism defined over $\overline {\mathbb Q}$?
Oct 6, 2014 at 13:39 history edited Pete L. Clark CC BY-SA 3.0
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Oct 6, 2014 at 13:07 history answered Pete L. Clark CC BY-SA 3.0