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Principal Schottky bundles over Riemann surfaces

  • A. C. Casimiro
  • S. Ferreira
  • C. Florentino
Original Paper
  • 21 Downloads

Abstract

We introduce and study (strict) Schottky G-bundles over a compact Riemann surface X, where G is a connected reductive algebraic group. Strict Schottky representations are shown to be related to branes in the moduli space of G-Higgs bundles over X, and we prove that all Schottky G-bundles have trivial topological type. Generalizing the Schottky moduli map introduced in Florentino (Manuscr Math 105:69–83, 2001) to the setting of principal bundles, we prove its local surjectivity at the good and unitary locus. Finally, we prove that the Schottky map is surjective onto the space of flat bundles for two special classes: when G is an abelian group over an arbitrary X, and the case of a general G-bundle over an elliptic curve.

Keywords

Representations of the fundamental group Character varieties Principal bundles Moduli spaces Riemann surfaces Schottky bundles Uniformization 

Mathematics Subject Classification

Primary 14H70 30F10 Secondary 32CXX 

Notes

Acknowledgements

We thank I. Biswas, E. Franco, P. B. Gothen, C. Meneses-Torres and A. Oliveira for several useful discussions on Schottky bundles and related subjects, and the referees for clarifying comments. The last author thanks the organizers of the Simons Center for Geometry and Physics workshop on Higgs bundles, and L. Schaposnik and D. Baraglia for details on their construction of (A,B,A) branes.

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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Departamento Matemática and Centro de Matemática e Aplicações, Faculdade de Ciências e TecnologiaUniversidade Nova de LisboaCaparicaPortugal
  2. 2.Escola Superior de Tecnologia e Gestão de LeiriaLeiriaPortugal
  3. 3.Departamento de Matemática, Faculdade de CiênciasUniv. de LisboaLisbonPortugal

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