Zariski Density of Monodromy Groups via a Picard–Lefschetz Type Formula. (20th February 2017) - Xu, Jinxing
Abstract: For the universal family of cyclic covers of projective spaces branched along hyperplane arrangements in general position, we consider its monodromy group acting on an eigenspace of the middle cohomology of the fiber. We prove the monodromy group is Zariski dense in the corresponding linear group. As an application, we show the fundamental group of the moduli space of hyperplane arrangements is large. It can be viewed as a degenerate analogy of Carlson-Toledo's result about the monodromy groups of smooth hypersurfaces [3 ]. The main ingredient in the proof is a Picard–Lefschetz type formula for a suitable degeneration of this family.