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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.

4 votes

Is there a Riemann-Roch like result for meromorphic differentials with all periods vanishing?

Let me address the concrete problem. If you have two forms like this, the difference would be holomorphic, thus a constant, so uniqueness is clear. For existence, suppose the points are $a$, $b$ and …
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