%0 Book Section
%T Moduli spaces of connections on a Riemann surface.
publisher International Press
%D 2010
%U 978-1-57146-195-7
%@ https://hdl.handle.net/20.500.14352/45436
%X Let E be a holomorphic vector bundle over a compact connected Riemann surface X. The vector bundle E admits a holomorphic projective connection if and only if for every holomorphic direct summand F of E of positive rank, the equality degree(E)=rank(E) = degree(F)=rank(F) holds. Fix a point x0 in X. There is a logarithmic connection on E, singular over x0 with residue ¡d n IdEx0 if and only if theequality degree(E)=rank(E) = degree(F)=rank(F) holds. Fix an integer n ¸ 2, and also ¯x an integer d coprime to n. Let M(n; d) denote the moduli space of logarithmicSL(n;C){connections on X singular of x0 with residue ¡ d nId. The isomorphism class of the variety M(n; d) determines the isomorphism class of the Riemann surface X.
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