Pullback and direct image of parabolic Higgs bundles and parabolic connections with symplectic and orthogonal structures

Abstract

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.