Zariski density of monodromy groups via Picard-Lefschetz type formula

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 eigen linear subspace of the middle cohomology of the fiber. We prove the monodromy group is Zariski dense in the corresponding linear group. It can be viewed as a degenerate analogy of Carlson-Toledo's result about the monodromy groups of smooth hypersurfaces [Duke Math. J. 97(3) (1999), 621-648]. The main ingredient in the proof is a Picard-Lefschetz type formula for a suitable degeneration of this family.

Reformatted author manuscript; corrigendum appended correcting the proof of Proposition 4.2. The main theorem statements are unchanged. 27 pages of the article and 5 pages of the corrigendum

References in corpus (3)

• Image of the Burau Representation at $d$-th Roots of unity
• Monodromy of Cyclic Coverings of the Projective Line
• On the monodromy of the moduli space of Calabi-Yau threefolds coming from eight planes in ${\mathbb{P}}^3$

Cited by in corpus (1)

• Remarks on eigenspectra of isolated singularities