Monodromy action on character varieties for Lefschetz pencils

Abstract

Given a Riemann surface Σ, let Γ {\subseteq} Mod(Σ) denote the monodromy subgroup of a family of complex curves homeomorphic to Σ, arising from a sufficently ample Lefschetz pencil. We establish that the group Γ acts with Zariski dense orbits or ergodically on certain character varieties for {π_1}(Σ). This answers a version of a Conjecture of Katzarkov, Pantev, and Simpson appearing in [KPS03].

25 pages, 5 figures