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Results tagged with ag.algebraic-geometry
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user 126243
Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
5
votes
0
answers
205
views
Asphericity of hypersurface complement in ${\mathbb C}^n$
How does one check that the following space is aspherical?
$X_n=\{(x_1,x_2,\ldots , x_n)\in {(\mathbb C^*)}^n\ |\ x_i\neq x_j\ and\ x_ix_j\neq 1\ for\ i\neq j\}$.
One way I can think of is to give …
- 585
4
votes
1
answer
308
views
Connectedness of Milnor fiber
Let $Q$ be a homogeneous polynomial in $n$ variables. Then it defines a locally trivial fiber bundle projection $Q:{\mathbb C}^n- Q^{-1}(0)\to {\mathbb C}-\{0\}$ (called Milnor fibration). Under what …
- 585
3
votes
1
answer
234
views
Applications of Thom's first isotopy lemma
Thom's first isotopy lemma says that given a smooth map $f:M\to P$ between smooth manifolds, and a closed Whitney stratified subset $S$ of $M$, such that
$f|_S:S\to P$ is proper and $f|_X:X\to P$ is a …
- 585
1
vote
0
answers
90
views
Cohomological dimension of the kernel of a homomorphism induced by a singular fibration
I have a very concrete question. Let $N={\Bbb C}-\{\pm 1\}$, and ${\Bbb Z}_2$ is acting on $N$ by rotation around $0$. Consider $M=\{(x,y)\in N^2\ |\ {\Bbb Z}_2x\neq {\Bbb Z}_2y\}$. Let $p:M\to N$ be …
- 585