On the moduli spaces of framed logarithmic connections on a Riemann surface

Biswas, Indranil; Inaba, Michi-aki; Komyo, Arata; Saito, Misato

doi:10.5802/crmath.199

Comptes Rendus. Mathématique

2021

DOI: 10.5802/crmath.199

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On the moduli spaces of framed logarithmic connections on a Riemann surface

Indranil Biswas¹,

Michi-aki Inaba²,

Arata Komyo³

et al.

Abstract: On the moduli spaces of framed logarithmic connections on a Riemann surface

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Cited by 2 publications

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The twistor geometry of parabolic structures in rank two

Simpson

2022

Proc Math Sci

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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 λconnections 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.

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The twistor geometry of parabolic structures in rank two

Simpson

2022

Proc Math Sci

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Twistor space for local systems on an open curve

Simpson

2024

Int. J. Math.

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Let [Formula: see text] be a smooth quasi-projective curve. We previously constructed a Deligne–Hitchin moduli space with Hecke gauge groupoid for connections of rank [Formula: see text]. We extend this construction to the case of any rank [Formula: see text], although still keeping a genericity hypothesis. The formal neighborhood of a preferred section corresponding to a tame harmonic bundle is governed by a mixed twistor structure.

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On the moduli spaces of framed logarithmic connections on a Riemann surface

Abstract: On the moduli spaces of framed logarithmic connections on a Riemann surface

Cited by 2 publications

References 15 publications

The twistor geometry of parabolic structures in rank two

The twistor geometry of parabolic structures in rank two

Twistor space for local systems on an open curve

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