Collapsing D-branes in one-parameter models and small/large radius duality

We finalize the study of collapsing D-branes in one-parameter models by completing the analysis of the associated hypergeometric hierarchy. This brings further evidence that the phenomenon of collapsing 6-branes at the mirror of the `conifold' point in IIA compactifications on one-parameter Calabi-Yau manifolds is generic. It also completes the reduction of the study of higher periods in one-parameter models to a few families which display characteristic behaviour. One of the models we consider displays an exotic form of small-large radius duality, which is a consequence of an ``accidental'' discrete symmetry of its moduli space. We discuss the implementation of this symmetry at the level of the associated type II string compactification and its action on D-brane states. We also argue that this model admits two special Lagrangian fibrations and that the symmetry can be understood as their exchange.