# Tagged Questions

**1**

vote

**1**answer

127 views

### lift of antiholomorphic involution of Riemann surface to its Jacobian's cohomology

Start from a connected closed Riemann surface $\Sigma_g,$
obtained as the (symmetric) covering of an open and/or unoriented surface
$\Sigma,$ namely $\Sigma=\Sigma_g/\Omega,$ where $\Omega$ is an ...

**0**

votes

**1**answer

175 views

### Reference for notation $H^0(C, mK)$

I am reading the draft of "Equations of Riemann Surfaces of Genus 4, 5 and 6 wih Large Automorphism groups" and the author starts using the notation $H^0(C, mK)$ on page 3, without explaining it. As ...

**12**

votes

**1**answer

454 views

### Essential uniqueness of the real-analytic structure on $\mathbb R$

It is well-known that any $C^k$-smooth $1$-manifold homeomorphic to $\mathbb R$ is $C^k$-diffeomorphic to $\mathbb R$. The cases of $k\in{\mathbb N}\cup$ {$\infty$} may all be handled similarly by ...

**3**

votes

**0**answers

152 views

### Branched Covers of a Two-sphere with Infinite Degree

I would like to ask the following question:
Let us consider the following branched cover $X_n$ of $\mathbb{P}^1$ that can be thought as a hyper-surface of $\mathbb{P}^1 \times \mathbb{P}^1$:
...

**3**

votes

**2**answers

488 views

### finite-dimensionality of cohomology groups on compact riemann surfaces

does the finite dimensionlity of the first cohomology group ($ H^1 $) of the sheaf of meromorphic sections of a holomorphic line bundle on a compact riemann surface follow easily from the finite ...

**3**

votes

**6**answers

917 views

### Dolbeault cohomology

Hello
I am trying to get a good book that explains the Dolbeault Cohomology, does anyone know of a good one?