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 a 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.
See also Hilbert's sixteenth problem Tropical geometry
References