Root lattices and pencils of varieties

this paper a particular pencil of K3 surfaces is investigated. The PicardFuchs equation, solutions, and the monoromy group are found. The paper of [17] gives the Picard-Fuchs equation for several families of elliptic curves. Similar methods are used in [13] and [14] to obtain the Picard-Fuchs equation for the case of certain pencils of K3 surfaces also. In these papers finding the Picard-Fuchs equation comes down to finding a recurrence relation for some sequence of combinatorially defined terms, e.g., in [5], recurrence relations are found for a n in the following cases: a n =