On the intersections of rational curves with cubic plane curves

Details On the intersections of rational curves with cubic plane curves On the intersections of rational curves with cubic plane curves

1995-11-08

arxiv.org/abs/alg-geom/9511006v3

Mathematics

Algebraic Geometry

14 pages plain TeX

Scientific paper

Let C be a smooth cubic curve in the complex projective plane. We show that for every positive integer k, there are only finite number of rational curves of degree k each intersects the cubic C at exactly one point. The number of such rational curves is known when k is 1, as a smooth cubic has 9 flexes points. This number seems to be closely related to the number of plane rational curves of degree k passing through 3k-1 general points, which has been computed.

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