# Tag Info

Accepted

### $S^3$ as cyclic branched cover of itself

The statement that for arbitrary K in $S^3$, if for some $n \ge 2$, the n-fold cyclic branched cover is $S^3$ (or in some versions, a homotopy 3-sphere) then K is the unknot, was known as the Smith ...
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• 10k

### Two ways to look at a double cover of the projective line

The smooth points on a cuspidal cubic curve in $\mathbb P^2$ can be given the structure of an algebraic group, just as is done for smooth cubic curves. If the tangent directions of the cuspidal point ...
• 46.7k
Accepted

### Monodromy representation of elementary simple covers

I am just writing my comments as an answer. For every subgroup $H$ of the symmetric group $\mathfrak{S}_n$, define a relation on $\{1,\dots,n\}$ by $a\sim b$ if either $a$ equals $b$ or if the ...

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### Books for learning branched coverings

You can have a look at Makoto Namba's book "Branched coverings and algebraic functions".
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### What is definition of branched covering?

At the top of page ten of this paper the authors write "the standard two-sheeted branched covering of the sphere by the torus, branched over four points which become the four boundary circles of ...
• 27k
1 vote
Accepted

### Unibranch points (definition for varieties over arbitrary field)

For a scheme $X$, say that $X$ is topologically unibranch at $x$ if $\mathop{Spec} O_{X,x}$ is geometrically unibranch (meaning that $O_{X,y}$ is geometrically unibranch at all generisations $y$ of $x$...
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1 vote

### Cohomology of ramified double cover of $\mathbb P^n$ (reference)

This is not an area of expertise for me, so forgive me if I didn't understand the question properly and hence this answer isn't on point. I think the original reference for this might be Lazarsfeld's ...
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