Nahm transformation for parabolic integrable connections on the\n projective line -- case of generic regular graded residues

2017/02/10 by Szilárd Szabó, Szabó, Szilárd
Mathematics · #14F40 #14H60 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1702.03306

openalex publication_date 2017/02/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a de Rham interpretation of Nahm's transform for certain parabolic\nharmonic bundles on the projective line and compare it to minimal\nFourier--Laplace transform of \D-modules. We give an algebraic\ndefinition of a parabolic structure on the transformed bundle and show that it\nis compatible with the transformed harmonic metric.\n

Citations

• The birational geometry of irregular Higgs bundles
• The Self-Duality Equations on a Riemann Surface

Related

• Nahm transform for integrable connections on the Riemann sphere
• Parabolic connections and stack of roots
• Isomonodromic deformations of logarithmic connections and stable\n parabolic vector bundles
• Fibrés paraboliques et champ des racines
• Moduli space of parabolic Λ-modules over a curve