The authors construct one parameter families of \(n\)-dimensional Calabi-Yau manifolds, which are complete intersections of toric varieties and which have a monodromy operator \(T\) such that \((T^N-\text{id})^{n+1}=0\) but \((T^N-\text{id})^n\neq 0\) for some \(N\in {\mathbb N}\). (The presence of \(N\) is explained by the well-known property of the operators of geometric monodromy their eigenvalues to be roots of unity; the two conditions imply that \(T\) has a Jordan block of size \(n+1\) which is the maximal possible.) In such a case one says that \(T\) is maximal unipotent.
The results are inspired by string theory in the B model which requires the existence of degenerations of Calabi-Yau manifolds with maximum unipotent monodromy. In string theory such a point in the moduli space is called a large radius limit (or large complex structure limit). The authors base their method of proof on the Clemens theory of monodromy and on the theory of mixed Hodge structures.