  The study of curved D-brane geometries in type II strings implies a general
relation between local singularities $\cx W$ of Calabi-Yau manifolds and
gravity free supersymmetric QFT's. The minimal supersymmetric case is described
by F-theory compactifications on $\cx W$ and can be used as a starting point to
define minimal supersymmetric heterotic string compactifications on compact
Calabi-Yau manifolds with holomorphic, stable gauge backgrounds. The geometric
construction generalizes to non-perturbative vacua with five-branes and
provides a framework to study non-perturbative dynamics of the heterotic
theory.
