Английская Википедия:Gudkov's conjecture
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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 <math>2d</math> obeys the congruence
- <math> p - n \equiv d^2\, (\!\bmod 8),</math>
where <math>p</math> is the number of positive ovals and <math>n</math> 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 <math>k-1</math>, where <math>k</math> is the number of maximal components of the curve.[1])
The theorem was proved by the combined works of Vladimir Arnold and Vladimir Rokhlin.[2][3][4]
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