Schottky uniformization and vector bundles over Riemann surfaces

Carlos Florentino

doi:10.1007/pl00005874

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Schottky uniformization and vector bundles over Riemann surfaces

Carlos Florentino

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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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Carlos Florentino. 2001-04-23. Schottky uniformization and vector bundles over Riemann surfaces. https://doi.org/10.1007/pl00005874

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