In algebraic geometry, is the dual of the dual curve the original curve? Why or why not?
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3$\begingroup$ This is a very classical result, true for hypersurfaces of any dimension; you'll find a proof in many places, including Chapter 1 of Dolgachev's book. MO is a site for questions about mathematics at research level, please consider using math.stackexchange.com instead. $\endgroup$– abxNov 14, 2015 at 6:05
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2$\begingroup$ Since the OP did not specify the ground field, I should point out that this is not always true in positive characteristic. A simple counterexample is of a conic in characteristic two. The dual is a line and the double dual a point. $\endgroup$– Felipe VolochNov 14, 2015 at 15:28
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$\begingroup$ Dolgachev's book does not have a proof. Theorem 1.2.2, the reflexivity theorem, is not proven. $\endgroup$– user2154420Apr 2, 2020 at 21:16
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This is claimed and proved as Theorem 1 here https://math.berkeley.edu/~monks/papers/DualityV3.pdf