Questions tagged [branched-covers]
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69
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Smoothness of the branch divisor and ramification on surfaces
Let $f \colon X \longrightarrow Y$ be a finite morphism of degree $n \geq 2$ between smooth compact, complex surfaces.
Let $B \subset Y$ be the branch divisor of $f$ and assume that the ...
- 65.7k
15
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1
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$S^3$ as cyclic branched cover of itself
In Chapter One of his notes (March 2002) Thurston says:
If $K$ is the trivial knot the cyclic branched covers are $S^3$. It seems intuitively obvious (but it is not known) that this is the only ...
- 606
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0
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Two transfers for ramified or branched covers
Let $\pi: X \rightarrow Y$ be a 2-fold branched cover of complex varieties. I know of (at least) two types of pushforwards associated to this situation:
If I'm not mistaken, there is a pushforward ...
- 13.3k
4
votes
1
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Flatness of Weil restriction
Let $X\rightarrow Y$ a ramified double cover of smooth projective curves, and let $$\mathcal G:=Res_{X/Y}(SL_n)$$
be the Weil restriction of the constant group scheme $SL_n$ over $X$.
Question: Is ...
- 1,871
6
votes
1
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Can you functorially "reconstruct" a branched cover of curves from its etale locus?
I'm sure this must be covered somewhere, but all the references I have only treat this in very special cases (mostly when working over fields).
Suppose $f : X\rightarrow S$ is smooth of finite ...
- 10k
8
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4
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Conditions for underlying space of an orbifold $\Bbb T^n/\Gamma$ to be a sphere?
Given a $n$-dimensional torus, is it always possible to find a discrete action to produce an orbifold such that its underlying space is the $n$-dimensional sphere? Or does it only happens for specific ...
- 437
5
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Definition and sigularity of Ramified covers
Let $X$ be a normal variety over $\mathbb{C}$.
In their book Birational geometry of algebraic varieties, Kollár and Mori define [Definition 2.50 and 2.51] a ramified m-th cyclic cover associate to a ...
- 3,392
2
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1
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Kummer Coverings
Let $L_1$, $\cdots$, $L_k$ be homogenous linear forms in three variables $z_0$, $z_1$, $z_2$ defining $k$ lines in $\mathbb{P}_{2}$. Consider the abelian extension $K
((L_2/L_1)^{1/n}, \cdots, (L_k/...
- 21
5
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3
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Heegaard Floer Homology of double branched cover
The question is the following:
Let $K\subset S^{3}$ be a knot, consider the double branched cover $Y$ of $S^{3}$ over $K$. We know $Y$ has a unique spin structure $\mathfrak{s}$, now the question is: ...
- 1,059
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Finite morphisms to projective space
Let $X$ be a projective variety of dimension n. Then there exists a finite surjective morphism $X \to \mathbf P^n$. Let $d$ be the minimal degree of such a finite surjective morphism.
Let $d^\prime ...
- 91
4
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To what extent does the branch locus determine the covering (Chisini's conjecture)?
Suppose that $X$ is a smooth projective surface over $\mathbb C$ and $f\colon X\to\mathbb P^2$ is a finite morphism branched over a curve $S\subset\mathbb P^2$. Assume in addition that all the ...
- 1,839
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1
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The cyclic branched covers of "simple" knots in $S^3$
Is there a convenient place in the literature where the geometric decompositions of cyclic branched covers of $S^3$ branched over "small" knots is recorded?
By small knots, I'm referring to things ...
- 43.5k
2
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branch locus of the discriminant map $\overline{\mathcal{H}}_{g',r} \to \overline{\mathcal{M}}_{g,n}$
Let $\overline{\mathcal{M}}_{g,n}$ be the moduli space of pointed, stable, genus $g$ curves. Let $\overline{\mathcal{H}}_{g',r}$ be the hurwitz space of cyclic covers of degree $r$ of genus $g$ curves ...
- 3,737
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2
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chern classes of push-pulled vector bundles
Let $f:X\to Y$ be a finite cover of smooth algebraic varieties, branched along a divisor $R\subset Y$. Let $E$ be a vector bundle on $Y$. What is the relation between the chern classes of $E$ and the ...
- 3,737
11
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2
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Orbifolds vs. branched covers
Forgive me if this is a basic question. I'm just learning about orbifolds, and covering spaces are my happy place for thinking about group actions.
If $M$ is a manifold and $G$ is a group acting ...
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