2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62074We define the C^*-action on moduli spaces of reductive representations of fundamental groups of quasi-compact Kaehler manifolds by solving Hermitian-Yang-Mills equation. As applications in algebraic geometry we show a non-abelian Hodge (p,q)-type theorem for families of quasi-projective manifolds. We also prove that any discrete sub group of a Lie group of rank >1 that is not of Hodge type can't be the fundamental group of a quasi-compact Kaehler manifold.This paper has been withdrawnAlgebraic GeometryDifferential Geometrytext