Alfaya Sánchez, David Biswas, Indranil 2025-09-26T15:26:06Z 2025-09-26T15:26:06Z 2023-11-01 1073-7928 https:doi.org10.1093imrnrnad193 Artículos en revistas We provide an explicit algebraic construction—for the pullback and direct image of parabolic bundles, parabolic Higgs bundles, and parabolic connections—through nonconstant maps between compact connected Riemann surfaces. We show that these constructions preserve semistability and polystability. We also prove that these constructions are compatible with the nonabelian Hodge correspondence. We provide an explicit algebraic construction—for the pullback and direct image of parabolic bundles, parabolic Higgs bundles, and parabolic connections—through nonconstant maps between compact connected Riemann surfaces. We show that these constructions preserve semistability and polystability. We also prove that these constructions are compatible with the nonabelian Hodge correspondence. application/octet-stream en-GB Revista: International Mathematics Research Notices, Periodo: 1, Volumen: online, Número: 22, Página inicial: 19546, Página final: 19591 Instituto de Investigación Tecnológica (IIT) Pullback and direct image of parabolic connections and parabolic Higgs bundles info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion info:eu-repo/semantics/openAccess Parabolic bundle, nonabelian Hodge correspondence, pullback, direct image, semistability Parabolic bundle, nonabelian Hodge correspondence, pullback, direct image, semistability