Pullback and direct image of parabolic connections and parabolic Higgs bundles

D. Alfaya, I. Biswas

International Mathematics Research Notices Vol. 2023, nº. 22, pp. 19546 - 19591

Resumen:

We provide an explicit algebraic construction—for the pullback and direct image of parabolic bundles, parabolic Higgs bundles, and parabolic connections—through nonconstant maps between compact connected Riemann surfaces. We show that these constructions preserve semistability and polystability. We also prove that these constructions are compatible with the nonabelian Hodge correspondence.

Resumen divulgativo:

Damos construcciones algebraicas explícitas para el pullback y la imagen directa de fibrados parabólicos, fibrados de Higgs parabólicos y conexiones parabólicas. Probamos que las construcciones preservan semiestabilidad y poliestabilidad y son compatibles con la correspondencia de Hodge no abeliana.

Palabras Clave: Parabolic bundle, nonabelian Hodge correspondence, pullback, direct image, semistability

Índice de impacto JCR y cuartil WoS: 1,000 - Q2 (2022)

Referencia DOI: https://doi.org/10.1093/imrn/rnad193

Publicado en papel: Noviembre 2023.

Publicado on-line: Agosto 2023.

Cita:
D. Alfaya, I. Biswas, Pullback and direct image of parabolic connections and parabolic Higgs bundles. International Mathematics Research Notices. Vol. 2023, nº. 22, pp. 19546 - 19591, Noviembre 2023. [Online: Agosto 2023]