Abstract
We obtain a recursive formula for the number of rational degree d curves in P3, whose image lies in a P2, intersecting r lines and s points, where r+2s=3d+2. This can be viewed as a family version of the classical question of counting rational curves in P2. We verify that our numbers are consistent with those obtained by T. Laarakker, where he studies the parallel question of counting δ-nodal degree d curves in P3 whose image lies inside a P2. Our numbers give evidence to support the conjecture, that the polynomials obtained by T. Laarakker are enumerative when d≥1+[δ2], which is analogous to the Göttsche threshold for counting nodal curves in P2.
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