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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.

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A basis of holomorphic differentials on Fermat curves

The automorphisms $a_1,a_2,a_3$ are part of a $\mathbb{Z}/p\mathbb{Z}\times\mathbb{Z}/p\mathbb{Z}$ action on $F_k$, which in turn induces an action on the space $H^0(\Omega^1_{F_k})$ of holomorphic di …
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5 votes
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Holomorphic vector bundles over a Riemann surface does not satisfy $\mathbf{AB2}$ but satisf...

(This should really be a comment on S. Carnahan's answer, but don't have enough reputation.) All coherent sheaves on a Riemann surface split into the direct sum of a torsion sheaf and a vector bundle …
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