In algebraic geometry, is the dual of the dual curve the original curve? Why or why not?


closed as off-topic by Alexey Ustinov, abx, Myshkin, Daniel Loughran, Stefan Kohl Nov 14 '15 at 10:06

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    $\begingroup$ 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. $\endgroup$ – abx Nov 14 '15 at 6:05
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    $\begingroup$ 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 Voloch Nov 14 '15 at 15:28

This is claimed and proved as Theorem 1 here https://math.berkeley.edu/~monks/papers/DualityV3.pdf


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