Summary:
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.
Spanish layman's summary:
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.
English layman's summary:
We prove that pullbacks and direct images of vector bundles, Higgs bundles and connections endowed with a parabolic symplectic (resp. orthogonal) structure inherit natural symplectic (resp. orthogonal) structures. These constructions are preserved through the nonabelian Hodge correspondence.
Keywords: 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.
JCR-JIF Impact Factor and WoS quartile: 0,700 - Q2 (2024)
DOI reference:
https://doi.org/10.1215/00192082-12506444
Published on paper: April 2026.
Published on-line: May 2026.
Citation:
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, April 2026. [Online: May 2026] doi: 10.1215/00192082-12506444
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