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Results tagged with riemann-surfaces
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user 7313
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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Reference for hyperelliptic curves
I was reading a paper the other day that said that all automorphisms of a hyperelliptic curve are liftings of automorphisms of $\mathbb{P}^1$ operating on the set of branch points.
Can someone point …
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Fuchsian groups and their normalizers
Let $\Gamma \leq PSL_2(\mathbb{R})$ be a Fuchsian group. What is the relation between $N(\Gamma) = \{ \alpha \in PSL_2(\mathbb{R}) \mid \alpha \Gamma \alpha^{-1} = \Gamma \}$ and $Aut(\Gamma \backslas …
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Fuchsian groups and automorphisms of Riemann surfaces
Let $\Gamma \subseteq PSL_2(\mathbb{R})$ be a Fuchsian group, possibly containing elliptic elements. Is it true that $N(\Gamma) / \Gamma$, where $N(\Gamma)$ the normalizer of $\Gamma$ in $PSL_2(\mathb …
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0
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Representation of the group of automorphisms on the holomorphic forms
Let $X$ be a compact Riemann surface and $G = Aut(X)$ be its group of automorphisms (biholomorphisms between $X$ and $X$). It is known that $G$ acts on the space $Harm(X)$ of all harmonic forms and al …
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