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Results tagged with riemann-surfaces
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user 318
Riemann surfaces(Riemannian surfaces) is one dimensional complex manifold. For questions about classical examples in complex analysis, complex geometry, surface topology.
23
votes
Accepted
Square root of the determinant line
There is no such isomorphism (at least for $g \geq 9$).
In
O. Randal-Williams, The Picard group of the moduli space of r-Spin Riemann surfaces. Advances in Mathematics 231 (1) (2012) 482-515.
I co …
- 18.2k
2
votes
Accepted
Homology dimension of the mapping class group of a surface with boundary
There is a fibration sequence
$$\mathbb{S}(\Sigma_g) \to \mathcal{M}_{g}^1 \to \mathcal{M}_g$$
where $\mathcal{M}_g$ is the moduli space of Riemann surfaces, $\mathcal{M}_{g}^1$ is the moduli space of …
- 18.2k
8
votes
2
answers
443
views
Approximating holomorphic maps by holomorphic embeddings
Let $\mathrm{Hol}^d(\Sigma, \mathbb{C} \mathbb{P}^n)$ denote the space of holomorphic maps of degree $d$ from a Riemann surface $\Sigma$ to complex projective space of dimension $n$. Let $\mathrm{HolE …
- 18.2k