I have been working on this and by Bezout I believe that if the line is to intersect a cubic in only one point it must do so with multiplicity 3. I am though unsure given a point $P$ on a cubic how I may define a line also incident with this point but not incident with the cubic again
2026-03-27 15:06:30.1774623990
Is it possible to define a projective line that intersects a projective cubic only once?
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Yes if the projective line comes inside intersecting at one point and leaving through the same point