# Tagged Questions

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### A question on Aut$(N)$ and Aut$(N/G)$

Let $N$ be a complex manifold and $G$ is a finite group freely acting on $N$. Define another complex manifold $M$ as $M=N/G$. I would like to study Aut$(M)$, the (holomorphic) automorphism group of ...
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### If a subspace is simply connected, then the space itself is simply connected

Let $X$ be a "nice" connected topological space. Let $U\subset X$ be a non-empty subspace. Suppose that $U$ is simply connected. Is $X$ simply connected? In my application, I'm actually thinking ...
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### Projective closure in the Zariski and Euclidean topologies

In Smith's An Invitation to Algebraic Geometry, following the definition of the projective closure of an affine variety, it was remarked that "the closure may be computed in either the Zariski ...
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### Fundamental group of the following disc

What is the fundamental group of the following space in $\mathbf C^n$? This is the topological space given by \{(x_1,\ldots,x_n)\in \mathbf C^n-\{0\} : \vert x_1\vert < 1, \ldots, \vert x_n\vert ...
### Why is $x^2$ +$y^2$ = 1, where $x$ and $y$ are complex numbers, a sphere?
I've heard $x^2 + y^2$ = 1, where $x$, $y$ are complex numbers, is supposed to be a sphere with two points removed, or also a cylinder. The problem is I've been trying to wrap my head around this for ...