Unipotent Schottky bundles on Riemann surfaces and complex tori

Details Unipotent Schottky bundles on Riemann surfaces and complex tori Unipotent Schottky bundles on Riemann surfaces and complex tori

2011-02-15

arxiv.org/abs/1102.3006v2

Mathematics

Algebraic Geometry

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Scientific paper

We study a natural map from representations of a free (resp. free abelian) group of rank g in GL_r(C), to holomorphic vector bundles of degree zero over a compact Riemann surface X of genus g (resp. complex torus X of dimension g). This map defines what is called a Schottky functor. Our main result is that this functor induces an equivalence between the category of unipotent representations of Schottky groups and the category of unipotent vector bundles on X. We also show that, over a complex torus, any vector or principal bundle with a flat holomorphic connection is Schottky.

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