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Gudkov's conjecture : ウィキペディア英語版 | Gudkov's conjecture In real algebraic geometry, Gudkov's conjecture, also called Gudkov’s congruence, (named after D. A. Gudkov) was a conjecture, and is now a theorem, which states that "a M-curve * of even degree ''2d'' obeys ''p'' – ''n'' ≡ ''d''2 (mod 8)", where ''p'' is the number of positive ovals and ''n'' the number of negative ovals of the M-curve. It was proved by the combined works of Vladimir Arnold and Vladimir Rokhlin. ==See also==
*Hilbert's sixteenth problem *Tropical geometry
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