All Questions
Tagged with branched-covers ramification
7
questions
4
votes
0
answers
402
views
Is there a Galois theory for deformations of curves?
I have some general questions about the deformations of Galois covers of curves. Suppose we are given a $G$-Galois cover $k[[z]]/k[[x]]$, where $k$ is algebraically closed of characteristic $p>0$. ...
- 245
2
votes
1
answer
412
views
Is the number of ramified coverings of given degree of a curve with prescribed branch divisor finite?
Let Y be a smooth projective curve over C and prescribe a branch divisor B on Y. I want to know if the number of coverings of Y of fixed degree and branched along B is finite. If so, why? Or, where is ...
- 23
8
votes
2
answers
1k
views
How to explicitly see the ramification over infinity
Take the equation $y^{d}=\Pi_{1}^{n}(x-t_{i})^{m_{i}}$ over $\mathbb{C}$. This affine equation gives a cyclic cover of $\mathbb{P}^{1}$. Now it is usually said without explanation that if the sum $\...
- 2,221
8
votes
1
answer
768
views
Question about local description of the branch locus
Let $\pi:Y\to X$ be a dominant, finite morphism of nonsingular varieties over an algebraically closed field $\Bbbk$. Assume furthermore that for all $Q\in Y$, with $P=\pi(Q)$, we have
$$\mathcal O_{Y,...
- 4,862
10
votes
2
answers
2k
views
Fibre cardinality of an unramified morphism
Let $\varphi: X \to Y$ be a finite, dominant, unramified morphism of varieties over an algebraically closed field. If necessary, we can assume $X$ and $Y$ to be nonsingular. I am trying to prove that
...
- 4,862
13
votes
2
answers
3k
views
Finite, Étale Morphism Of Varieties
I have a, probably very simple, question: My intuition tells me that the following statement should be true, but I couldn't find it anywhere and I wanted to make sure I am not missing something.
Let $...
- 4,862
28
votes
5
answers
7k
views
Higher dimensional version of the Hurwitz formula?
In Hartshorne IV.2, notions related to ramification and branching are introduced, but only for curves. The main result is the Hurwitz formula.
Now if you have a finite surjective morphism between ...
- 4,862