  The topological string partition function Z=exp(lambda^{2g-2} F_g) is
calculated on a compact Calabi-Yau M. The F_g fulfill the holomorphic anomaly
equations, which imply that Z transforms as a wave function on the symplectic
space H^3(M,Z). This defines it everywhere in the moduli space of M along with
preferred local coordinates. Modular properties of the sections F_g as well as
local constraints from the 4d effective action allow us to fix Z to a large
extend. Currently with a newly found gap condition at the conifold, regularity
at the orbifold and the most naive bounds from Castelnuovos theory, we can
provide the boundary data, which specify Z, e.g. up to genus 51 for the
quintic.
