All Questions

What is an example of a branched covering map between Riemann surfaces of infinite degree? i.e. something like a branched version of the exponential map $exp: \mathbb{C} \to \mathbb{C}^*$. Thanks!

I was listening to the lecture "Graphs from the point of view of Riemann surfaces" by Prof. Alexander Mednykh. I am looking for references for the basics of this topic. Any kind of ...

I am trying to visualize the genus-two Riemann surface given by the curve $$ y^3 = \frac{(x-x_1)(x-x_2)}{(x-x_3)(x-x_4)}. $$ We can regard this surface as a three-fold cover of the sphere with four ...

Let $Y$ be a compact Riemann surface and $B$ a finite subset of $Y$. It is a standard fact that isomorphism classes of holomorphic ramified covers $f:X\rightarrow Y$ of degree $d$ with branch points ...

Suppose I have a function $Q(z)$ of a complex variable $z\in\mathbb P^1$, possessing square root type branch points at the positions $\left\{z_i\right\}_{i=1}^{2M}$. I know that the Riemann surface $\...

Let $f:X\rightarrow Y$ be a ramified cover of Riemann surfaces or algebraic curves over $\mathbb{C}$. My question is can one in terms of the ramification data of $f$, determine whether the cover is ...