2021/10/23 by Carlos Simpson, Simpson, Carlos
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology
paper · doi:10.48550/arxiv.2110.12300
openalex publication_date 2021/10/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let X be a quasi-projective curve, compactified to (Y,D) with X=Y-D. We construct a Deligne-Hitchin twistor space out of moduli spaces of framed λ-connections of rank 2 over Y with logarithmic singularities and quasi-parabolic structure along D. To do this, one should divide by a Hecke-gauge groupoid. Tame harmonic bundles on X give preferred sections, and the relative tangent bundle along a preferred section has a mixed twistor structure with weights 0,1,2. The weight 2 piece corresponds to the deformations of the KMS structure including parabolic weights and the residues of the λ-connection.