The twistor geometry of parabolic structures in rank two

Carlos Simpson (1)

1 LJAD - Laboratoire Jean Alexandre Dieudonné

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 $\lambda$-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 $\lambda$-connection.

Mots clés: Parabolic structure; Moduli space; Twistor space; Logarithmic connection; Higgs bundle.

Domaines: Géométrie algébrique [math.AG]

Carlos Simpson. The twistor geometry of parabolic structures in rank two. Proceedings Mathematical Sciences, 2022, Special Issue in Memory of Professor C S Seshadri, 132 (2), pp.Article 54. ⟨10.1007/s12044-022-00696-1⟩. ⟨hal-03563729⟩