Alfaya Sánchez, David Biswas, Indranil Machu, Francois Xavier 2026-06-04T04:32:37Z 2026-06-04T04:32:37Z 2026-04-01 0019-2082 https://doi.org/10.1215/00192082-12506444 http://hdl.handle.net/11531/110415 Artículos en revistas Given a symplectic (resp. orthogonal) parabolic vector bundle over a compact Riemann surface, we prove that its pullback and direct image through a map between compact Riemann surfaces inherit a natural symplectic (resp. orthogonal) structure. If the parabolic bundle is endowed with a parabolic Higgs field or a parabolic connection that are compatible with the symplectic (resp. orthogonal) structure, then its pullback and direct image are also compatible with the resulting symplectic (resp. orthogonal) structure. We also show that these constructions are preserved through the nonabelian Hodge correspondence. Given a symplectic (resp. orthogonal) parabolic vector bundle over a compact Riemann surface, we prove that its pullback and direct image through a map between compact Riemann surfaces inherit a natural symplectic (resp. orthogonal) structure. If the parabolic bundle is endowed with a parabolic Higgs field or a parabolic connection that are compatible with the symplectic (resp. orthogonal) structure, then its pullback and direct image are also compatible with the resulting symplectic (resp. orthogonal) structure. We also show that these constructions are preserved through the nonabelian Hodge correspondence. application/pdf en-GB Revista: Illinois Journal of Mathematics, Periodo: 1, Volumen: online, Número: 1, Página inicial: 53, Página final: 76 Instituto de Investigación Tecnológica (IIT) Pullback and direct image of parabolic Higgs bundles and parabolic connections with symplectic and orthogonal structures info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion info:eu-repo/semantics/openAccess Parabolic symplectic bundle, parabolic orthogonal bundle, nonabelian Hodge correspondence, pullback, direct image, semistability; Fibrado simpléctico parabólico, fibrado ortogonal parabólico, correspondencia de Hodge no abeliana, imagen directa, semiestabilidad. Parabolic symplectic bundle, parabolic orthogonal bundle, nonabelian Hodge correspondence, pullback, direct image, semistability; Fibrado simpléctico parabólico, fibrado ortogonal parabólico, correspondencia de Hodge no abeliana, imagen directa, semiestabilidad.