Abstract
We review several aspects of heterotic, type II, F-theory, and M-theory compactifications on Calabi-Yau three-folds and fourfolds. In the context of dualities we focus on the heterotic gauge structure determined by the various types of fibration relevant in the framework of heterotic/type II duality in D=4 as well as 4D F-theory. We also consider transitions between Calabi-Yau manifolds in both three and four dimensions and review some of the consequences for the behavior of the superpotential.
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