Generating functions for the number of curves on abelian surfaces

Let X be an Abelian surface and C a holomorphic curve in X representing a primitive homology class. The space of genus g curves in the class of C is g dimensional. We count the number of such curves that pass through g generic points and we also count the number of curves in the fixed linear system |C| passing through g -2 generic points. These two numbers, (defined appropriately) only depend on n and g where n = CC 2 + 1 -g and not on the particular X or C (n is the number of nodes when a curve is nodal and reduced).