scientific article; zbMATH DE number 3805919

zbMath0511.30034MaRDI QIDQ4750091

Gerd Faltings

Publication date: 1983

Full work available at URL: http://www.numdam.org/item?id=CM_1983__48_2_223_0

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zbMATH Keywords

Galois covering of real algebraic curvemonodromy-group of connectionpermissible connection for uniformization datumreal monodromyrepresentation of discrete projective real 2-group

Mathematics Subject Classification ID

Compact Riemann surfaces and uniformization (30F10) Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) (32G15) Special algebraic curves and curves of low genus (14H45) Discrete subgroups of Lie groups (22E40) Coverings of curves, fundamental group (14H30) Connections (general theory) (53C05) Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) (30F35) Algebraic functions and function fields in algebraic geometry (14H05) Projective connections (53B10) Real algebraic and real-analytic geometry (14Pxx)

Related Items (19)

On Schottky and Koebe-like uniformizations ⋮ Algebraic representations of Teichmüller space ⋮ The grafting map of Teichmüller space ⋮ Branched projective structures with Fuchsian holonomy ⋮ Analytic Langlands correspondence for \(PGL_2\) on \(\mathbb{P}^1\) with parabolic structures over local fields ⋮ Real slices of \(\mathrm{SL}(r,\mathbb{C})\)-opers ⋮ Automorphic functions on moduli spaces of bundles on curves over local fields: a survey ⋮ Bers' simultaneous uniformization and the intersection of Poincaré holonomy varieties ⋮ Gauge theory and the analytic form of the geometric Langlands program ⋮ Real projective structures on Riemann surfaces and new hyper-Kähler manifolds ⋮ The monodromy of meromorphic projective structures ⋮ Flat Affine, Projective and Conformal Structures on Manifolds: A Historical Perspective ⋮ Asymptoticity of grafting and Teichmüller rays ⋮ Lyapunov exponents, holomorphic flat bundles and de Rham moduli space ⋮ Complex earthquakes and Teichmüller theory ⋮ Real projective connections, V. I. Smirnov's approach, and black-hole-type solutions of the Liouville equation ⋮ Some special families of rank-2 representations of \(\pi _1\) of compact Riemann surfaces ⋮ Extended monodromy for bordered surfaces ⋮ Differential operators on complex manifolds with a flat projective structure

Cites Work

• The real analytic theory of Teichmüller space
• Hall-order differentials on Riemann surfaces
• Special coordinate coverings of Riemann surfaces
• Vorlesungen über die Hypergeometrische Funktion
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