On the monodromy of elliptic surfaces

Abstract

There have been several constructions of family of varieties with exceptional monodromy group. In most cases, these constructions give Hodge structures with high weight(Hodge numbers spread out). N. Katz was the first to obtain Hodge structures with low weight(Hodge numbers equal to (2,3,2)) and geometric monodromy group G2. In this article I will give an alternative description of Katz's construction and give an extension of his result.