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Riemann surfaces(Riemannian surfaces) is one dimensional complex manifold. For questions about classical examples in complex analysis, complex geometry, surface topology.
7
votes
Accepted
Higgs fields whose determinant have only simple zeros
The statement is easily checked to be true for very stable bundles, so when you look for a counter example you will need to look for a wobbly (i.e. stable but not very stable) bundle.
Suppose that $ …
13
votes
Accepted
Representations of surface groups via holomorphic connections
This question is addressed in a very recent paper of Bogomolov-Soloviev-Yotov (I don't think it is on the web yet). Among many interesting things they prove that the map from the moduli space of pairs …