Schottky uniformization and vector bundles over Riemann surfaces

Details Schottky uniformization and vector bundles over Riemann surfaces Schottky uniformization and vector bundles over Riemann surfaces

2001-04-23

arxiv.org/abs/math/0104211v1

Mathematics

Differential Geometry

16 pages; AMSLatex

Scientific paper

We study a natural map from representations of a free group of rank g in GL(n,C), to holomorphic vector bundles of degree 0 over a compact Riemann surface X of genus g, associated with a Schottky uniformization of X. Maximally unstable flat bundles are shown to arise in this way. We give a necessary and sufficient condition for this map to be a submersion, when restricted to representations producing stable bundles. Using a generalized version of Riemann's bilinear relations, this condition is shown to be true on the subspace of unitary Schottky representations.

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