Abstract
We obtain a recursive formula for the number of rational curves of degree d in CP2, that pass through 3d+1−m generic points and that have an m-fold singular point. The special case of counting curves with a triple point was solved earlier by other authors. We obtain the formula by considering a family version of Kontsevich's recursion formula, in contrast to the excess intersection theoretic approach of others. A large number of low degree cases have been worked out explicitly.
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