Monodromy action on character varieties for Lefschetz pencils
Ishan Banerjee
Abstract
Given a Riemann surface Σ, let Γ ⊂eq 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 π1(Σ). This answers a version of a Conjecture of Katzarkov, Pantev, and Simpson appearing in [KPS03].
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