Counting curves with modular forms Original Research Article

We consider the type IIA string compactified on the Calabi-Yau space given by a degree 12 hypersurface in the weighted projective space P4(1,1,2,2,6). We express the prepotential of the low-energy effective supergravity theory in terms of a set of functions that transform covariantly under PSL(2, Z) modular transformations. These functions are then determined by monodromy properties, by singularities at the massless monopole point of the moduli space, and by S → T exchange symmetry.