We study the superpotential of a certain class of N=1 supersymmetric type II
compactifications with fluxes and D-branes. We show that it has an important
two-dimensional meaning in terms of a chiral ring of the topologically twisted
theory on the world-sheet. In the open-closed string B-model, this chiral ring
is isomorphic to a certain relative cohomology group V, which is the
appropriate mathematical concept to deal with both the open and closed string
sectors. The family of mixed Hodge structures on V then implies for the
superpotential to have a certain geometric structure. This structure represents
a holomorphic, N=1 supersymmetric generalization of the well-known N=2 special
geometry. It defines an integrable connection on the topological family of
open-closed B-models, and a set of special coordinates on the space \cal M of
vev's in N=1 chiral multiplets. We show that it can be given a very concrete
and simple realization for linear sigma models, which leads to a powerful and
systematic method for computing the exact non-perturbative N=1 superpotentials
for a broad class of toric D-brane geometries.Comment: 40p, harvmac-
