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 com pleting the analysis of the associated hypergeometric hierarchy. This bring s further evidence that the phenomenon of collapsing 6-branes at the mirror of the 'conifold' point in IIA compactifications on one-parameter Calabi-Y au manifolds is generic. It also completes the reduction of the study of hi gher periods in one-parameter models to a few families which display charac teristic behaviour. One of the models we consider displays an exotic form o f small-large radius duality, which is a consequence of an "accidental" dis crete symmetry of its moduli space. We discuss the implementation of this s ymmetry 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 spec ial Lagrangian fibrations and that the symmetry can be understood as their exchange. (C) 2001 Published by Elsevier Science B.V.