Enumeration of curves with one singular point

In this paper we obtain an explicit formula for the number of curves in P2, of degree d, passing through (d(d+3)/2−k) generic points and having a singularity X, where X is of type Ak≤7,Dk≤7 or Ek≤7. Our method comprises of expressing the enumerative problem as the Euler class of an appropriate bundle and using a purely topological method to compute the degenerate contribution to the Euler class. These numbers have also been computed by M. Kazarian using the existence of universal formulas for Thom polynomials.