Can someone explain to me why a cubic curve in a projective plane always meets a line three times?
2026-03-28 16:13:36.1774714416
Why a cubic plane curve meets a line three times?
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Consider changing the coordinates so that the line in question is the $x$ axis. Then you are just looking for the roots of a cubic equation. If you are working over an algebraically closed field then there will be three roots.