2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60829In this paper we study the monodromy action on the first Betti and de Rham non-abelian cohomology arising from a family of smooth curves. We describe sufficient conditions for the existence of a Zariski dense monodromy orbit. In particular we show that for a Lefschetz pencil of sufficiently high degree the monodromy action is dense.LaTeX2e, 48 pages, Version substantially revised for publication. A gap in the proof of the density for Lefschetz pencils is fixed. The case of hyperelliptic monodromy is also treated in detailAlgebraic Geometrytext