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Let $F\to M$ be a holomorphic vector bundle over a complex manifold $M$ and let $s:M\to F$ be a no-zero section. Let $E$ be the complexification of $F$, and suppose that $E$ admits a holomorphic ...

Has any work been done on the description of (finite rank) holomorphic vector bundles over Riemann surfaces of infinite genus? Is there a theory of moduli spaces of such objects? This question is ...