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

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.

URI

https://doi.org/10.1215/00192082-12506444
http://hdl.handle.net/11531/110415

Tipo de Actividad

Artículos en revistas

ISSN

0019-2082

Materias/ categorías / ODS

Instituto de Investigación Tecnológica (IIT)

Palabras Clave

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.

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