Principal Schottky bundles over Riemann surfaces

A. C. Casimiro, S. Ferreira, C. Florentino

Research output: Contribution to journalArticle

1 Citation (Scopus)

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.

Original languageEnglish
Pages (from-to)379-409
JournalGeometriae Dedicata
Early online date18 Oct 2018
DOIs
Publication statusPublished - 1 Aug 2019

Fingerprint

Riemann Surface
Bundle
Higgs Bundles
Surjectivity
Principal Bundle
Reductive Group
Algebraic Groups
Branes
Moduli Space
Elliptic Curves
Abelian group
Locus
Modulus
Trivial
Arbitrary

Keywords

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

Cite this

Casimiro, A. C. ; Ferreira, S. ; Florentino, C. / Principal Schottky bundles over Riemann surfaces. In: Geometriae Dedicata. 2019 ; pp. 379-409.
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Principal Schottky bundles over Riemann surfaces. / Casimiro, A. C.; Ferreira, S.; Florentino, C.

In: Geometriae Dedicata, 01.08.2019, p. 379-409.

Research output: Contribution to journalArticle

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