On the monodromy of elliptic surfaces

TL;DR

This paper explores the monodromy of elliptic surfaces, providing an alternative description of Katz's construction that yields low-weight Hodge structures with G2 monodromy, extending previous results.

Contribution

It offers a new perspective on Katz's construction and extends the understanding of monodromy groups in elliptic surfaces.

Findings

Alternative description of Katz's construction

Extension of Katz's results to new cases

Identification of G2 as geometric monodromy group

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.