Questions tagged [branched-covers]
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69
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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
6
votes
0
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301
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degenerating surface II
In degenerating surface, Robert Bryant give us an example of a sequence of minimal immersions which converges (in $C^2$- topology) to $z\mapsto z^{2k+1}$ on the unit disc $\mathbb{D}$. My question is ...
- 924
1
vote
1
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Manin-Drinfeld and constructing a finite morphism with two given ramification points
Fix a smooth projective connected curve $X$ over $\overline{\mathbf{Q}}$ of genus $g\geq 1$ and distinct points $x,y \in X$ such that $x-y$ has infinite order in the Jacobian.
Can we always find a ...
- 9,447
6
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2
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degenerating surface
Hi,
i have a sequence of immersed disc $u_n: \mathbb{D} \rightarrow \mathbb{R}^3$ which converge to a singular cover of the disc: $z^k$ for $k\geq 2$, moreprecisely $u_n \rightarrow z^k$ in $C^2(\...
- 924
2
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1
answer
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Comparing heights of rational points on curves through covers
Let $a$ be a closed point in $\mathbf{P}^1_{\overline{\mathbf{Q}}}$.
Let $Y \cong \mathbf{P}^1_{\overline{\mathbf{Q}}} $ and let $\pi:Y\to \mathbf{P}^1_{\overline{\mathbf{Q}}}$ be a finite morphism ...
- 23
13
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2
answers
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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
3
votes
0
answers
466
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cardinality of the fibre of a constantly branched, finite morphism over the branch locus
Let $\pi:Y\to X$ be a Galois cover, i.e. a finite morphism of nonsingular varieties over an algebraically closed field $\Bbbk$ such that $K(X)\hookrightarrow K(Y)$ is Galois. Let $H\subset X$ be the ...
- 4,862
28
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5
answers
7k
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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
35
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4
answers
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Curves which are not covers of P^1 with four branch points
The following interesting question came up in a discussion I was having with Alex Wright.
Suppose given a branched cover C -> P^1 with four branch points. It's not hard to see that the field of ...
- 19.1k