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Results tagged with riemann-surfaces
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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.
36
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If Spec Z is like a Riemann surface, what's the analogue of integration along a contour?
Rings of functions on a nonsingular algebraic curve (which, over $\mathbb{C}$, are holomorphic functions on a compact Riemann surface) and rings of integers in number fields are both examples of Dedek …
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How do you recover the structure of the upper half plane from its description as a coset space?
This is maybe a dumb question. $SL_2(\mathbb{R})$ has a natural action on the upper half plane $\mathbb{H}$ which is transitive with stabilizer isomorphic to $SO_2(\mathbb{R})$. For this reason, peo …
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"Physical" construction of nonconstant meromorphic functions on compact Riemann surfaces?
Miranda's book on Riemann surfaces ignores the analytical details of proving that compact Riemann surfaces admit nonconstant meromorphic functions, preferring instead to work out the algebraic consequ …
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