Branched Structures and Affine and Projective Bundles on Riemann Surfaces

DOI10.2307/1996458zbMath0278.30024OpenAlexW4254775652MaRDI QIDQ4405438

Richard Mandelbaum

Publication date: 1973

Full work available at URL: https://doi.org/10.2307/1996458

Mathematics Subject Classification ID

Compact Riemann surfaces and uniformization (30F10) Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) (32G15) Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) (30F35)

Related Items (18)

Liouville and Toda field theories on Riemann surfaces ⋮ Transversely holomorphic branched Cartan geometry ⋮ Holomorphic G-Structures and Foliated Cartan Geometries on Compact Complex Manifolds ⋮ Branched projective structures with Fuchsian holonomy ⋮ Mapping class group dynamics and the holonomy of branched affine structures ⋮ Branched projective structures, branched \(\mathrm{SO}(3,\mathbb{C})\)-opers and logarithmic connections on jet bundle ⋮ Stieltjes-Bethe equations in higher genus and branched coverings with even ramifications ⋮ Pictorial representation for antisymmetric eigenfunctions of PS-3 integral equations ⋮ Generalized holomorphic Cartan geometries ⋮ Local deformations of branched projective structures: Schiffer variations and the Teichmüller map ⋮ Dilation surfaces and their Veech groups ⋮ Unstable bundles and branched structures on Riemann surfaces ⋮ Monodromy groups and linearly polymorphic functions ⋮ Irreducible cone spherical metrics and stable extensions of two line bundles ⋮ Summing over geometries in string theory ⋮ A uniqueness theorem for deformations of Fuchsian groups ⋮ Branched projective structures on a Riemann surface and logarithmic connections ⋮ Uniformization of branched surfaces and Higgs bundles

Cites Work

• On deformations of complex analytic structures. I
• Hall-order differentials on Riemann surfaces
• Special coordinate coverings of Riemann surfaces
• Connections and conformal mapping
• Holomorphic fiber bundles over Riemann surfaces
• On holomorphic families of fiber bundles over the Riemannian sphere
• Branched Structures on Riemann Surfaces
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