  I give a conjectural generating function for the numbers of $\delta$-nodal
curves in a linear system of dimension $\delta$ on an algebraic surface. It
reproduces the results of Vainsencher for the case $\delta\le 6$ and
Kleiman-Piene for the case $\delta\le 8$. The numbers of curves are expressed
in terms of five universal power series, three of which I give explicitly as
quasimodular forms. This gives in particular the numbers of curves of arbitrary
genus on a K3 surface and an abelian surface in terms of quasimodular forms,
generalizing the formula of Yau-Zaslow for rational curves on K3 surfaces. The
coefficients of the other two power series can be determined by comparing with
the recursive formulas of Caporaso-Harris for the Severi degrees in $\P_2$. We
verify the conjecture for genus 2 curves on an abelian surface. We also discuss
a link of this problem with Hilbert schemes of points.
