Description
Title: Families of G-curves and maximal monodromy
Abstract: Maximality results for the monodromy of families of algebraic varieties are widely studied in algebraic geometry. In this talk, we study the monodromy of families of Galois coverings of curves. The natural action of the Galois group G on cohomology induces a decomposition of the associated variation of Hodge structures, and under a certain assumption on this decomposition, we prove that the algebraic monodromy group is maximal. As an application, we analyse positive-dimensional totally geodesic subvarieties of Ag arising from such families.