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About: Gudkov's conjecture     Goto   Sponge   NotDistinct   Permalink

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In real algebraic geometry, Gudkov's conjecture, also called Gudkov’s congruence, (named after Dmitry Gudkov) was a conjecture, and is now a theorem, which states that an M-curve of even degree obeys the congruence where is the number of positive ovals and the number of negative ovals of the M-curve. (Here, the term M-curve stands for "maximal curve"; it means a smooth algebraic curve over the reals whose genus is , where is the number of maximal components of the curve.) The theorem was proved by the combined works of Vladimir Arnold and Vladimir Rokhlin.