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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 $ …
Tony Pantev's user avatar
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13 votes
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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 …
Tony Pantev's user avatar
  • 6,239