Abstract:
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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Received: 13 June 2000 / Revised version: 29 December 2000
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Florentino, C. Schottky uniformization¶and vector bundles over Riemann surfaces. manuscripta math. 105, 69–83 (2001). https://doi.org/10.1007/PL00005874
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DOI: https://doi.org/10.1007/PL00005874