Target Space Duality of Calabi–Yau Spaces with Two Moduli

In the context of superstring compactifications on Calabi–Yau threefolds, we consider the Picard–Fuchs equations that are obeyed by the periods of the holomorphic three-form. We review, focusing on an example with two moduli, some powerful algebro-geometric techniques for computing the monodromy group of these equations, which is closely related to the target space duality group. For the example investigated, the latter is shown to be given by a three-dimensional representation of a central extension of $B_5$, the braid group on five strands.