1. The twistor geometry of parabolic structures in rank two
- Author
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Carlos Simpson, Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), This material is based upon work supported by a grant from the Institute for Advanced Study.Supported by the International Centre for Theoretical Sciences program ICTS/mbrs2020/02., ANR-19-P3IA-0002,3IA@cote d'azur,3IA Côte d'Azur(2019), and European Project: 670624,H2020,ERC-2014-ADG,DuaLL(2015)
- Subjects
General Mathematics ,MSC 2010 Primary 14D21, 32J25 ,Secondary 14C30, 14F35 ,Logarithmic connection ,Moduli space ,Twistor space ,Mathematics - Algebraic Geometry ,Mathematics::Algebraic Geometry ,FOS: Mathematics ,Mathematics::Differential Geometry ,Higgs bundle ,[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG] ,Parabolic structure ,Algebraic Geometry (math.AG) ,Mathematics::Symplectic Geometry - Abstract
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., Comment: minor changes and a reference
- Published
- 2022