For any compact Riemann surface of positive genus and any irrational slope θ, the colimit of stable bundles whose slopes are even convergents of θ completes to a holomorphic Hilbert bundle with a Hermitian-Einstein metric.
Curvature of vector bundles associated to holomorphic fibrations
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Constructing stable Hilbert bundles via Diophantine approximation
For any compact Riemann surface of positive genus and any irrational slope θ, the colimit of stable bundles whose slopes are even convergents of θ completes to a holomorphic Hilbert bundle with a Hermitian-Einstein metric.