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

Summary:

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.

Spanish layman's summary:

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.

English layman's summary:

We provide an explicit algebraic construction for the pullback and direct image of parabolic bundles, parabolic Higgs bundles and parabolic connections. We show that these constructions preserve semistability and polystability and that they are compatible with the nonabelian Hodge correspondence.

Keywords: Parabolic bundle, nonabelian Hodge correspondence, pullback, direct image, semistability

JCR Impact Factor and WoS quartile: 1,000 - Q2 (2022)

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

Published on paper: November 2023.

Published on-line: August 2023.

Citation:
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, November 2023. [Online: August 2023]