  We show how certain non-perturbative superpotentials W, which are the
two-dimensional analogs of the Seiberg-Witten prepotential in 4d, can be
computed via geometric engineering from 4-folds. We analyze an explicit example
for which the relevant compact geometry of the 4-fold is given by $P^1$ fibered
over $P^2$. In the field theory limit, this gives an effective U(1) gauge
theory with N=(2,2) supersymmetry in two dimensions. We find that the analog of
the SW curve is a K3 surface, and that the complex FI coupling is given by the
modular parameter of this surface. The FI potential itself coincides with the
middle period of a meromorphic differential. However, it only shows up in the
effective action if a certain 4-flux is switched on, and then supersymmetry
appears to be non-perturbatively broken. This can be avoided by tuning the bare
FI coupling by hand, in which case the supersymmetric minimum naturally
corresponds to a singular K3.
