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

D. Alfaya, I. Biswas, F.X. Machu

Illinois Journal of Mathematics Vol. 70, nº. 1, pp. 53 - 76

Resumen:

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.

Resumen divulgativo:

Probamos que los pullbacks e imágenes directas de fibrados vectoriales, fibrados de Higgs y conexiones con estructura simpléctica (resp. ortogonal) parabólica heredan estructuras simplécticas (resp. ortogonales) naturales. Estas construcciones se preservan en la correspondencia de Hodge no abeliana.

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.

Índice de impacto JCR-JIF y cuartil WoS: 0,700 - Q2 (2024)

Referencia DOI: https://doi.org/10.1215/00192082-12506444

Publicado en papel: Abril 2026.

Publicado on-line: Mayo 2026.

Cita:
D. Alfaya, I. Biswas, F.X. Machu, "Pullback and direct image of parabolic Higgs bundles and parabolic connections with symplectic and orthogonal structures", Illinois Journal of Mathematics, Vol. 70, nº. 1, pp. 53 - 76, Abril 2026. [Online: Mayo 2026] doi: 10.1215/00192082-12506444