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visits member for 2 years, 8 months
seen Nov 22 at 5:52

Nov
22
asked If $V$ is a quasi-affine variety, the algebra $k[V]$ is isomorphic to a subalgebra of a finitely generated $k$-algebra?
Nov
18
comment Why is $f(X)$ open or closed if $f:X\to\mathbb{A}^1(k)$ is regular?
Thanks again for your help!
Nov
18
accepted Why is $f(X)$ open or closed if $f:X\to\mathbb{A}^1(k)$ is regular?
Nov
17
comment Why is $f(X)$ open or closed if $f:X\to\mathbb{A}^1(k)$ is regular?
Thanks Georges. If $f$ is constant on each irreducible component of $X$, is it fair to say $f(X)$ is a finite number of points, hence closed?
Nov
17
comment Why is $f(X)$ open or closed if $f:X\to\mathbb{A}^1(k)$ is regular?
@MarianoSuárez-Alvarez I was just editing the question to make it more precise. I thought it had to be either open or closed, but it turns out it's just open. Also, I haven't read of Chevalley's theorem yet, so I'm wondering if there are more low-level explanations.
Nov
17
revised Why is $f(X)$ open or closed if $f:X\to\mathbb{A}^1(k)$ is regular?
edited tags
Nov
4
asked Why is $f(X)$ open or closed if $f:X\to\mathbb{A}^1(k)$ is regular?
Nov
4
accepted Is $\{(x,y,z,0)\in\mathbb{R}^4:x^4+y^2+z^2=1\}$ diffeomorphic to $S^2$?
Aug
10
comment Is $\{(x,y,z,0)\in\mathbb{R}^4:x^4+y^2+z^2=1\}$ diffeomorphic to $S^2$?
Oh, you're setting $\pi^{-1}(x,y,z)=(kx,ky,kz)$ and solving for $k$ under the condition that $(kx)^4+(ky)^2+(kz)^2=1$?
Aug
10
comment Is $\{(x,y,z,0)\in\mathbb{R}^4:x^4+y^2+z^2=1\}$ diffeomorphic to $S^2$?
What lead you to set $k^4x^4+k^2(1-x^2)=1$? I solved for $k$ to find $k=\pm\sqrt{\frac{x^2-1\pm\sqrt{1-2x^2+5x^4}}{2x^4}}$? Which kind of looks like what you wrote.
Aug
10
comment Is $\{(x,y,z,0)\in\mathbb{R}^4:x^4+y^2+z^2=1\}$ diffeomorphic to $S^2$?
Thanks! What is a "scale ratio" function? Is there a source to learn this technique? It seems useful.
Aug
10
comment Is $\{(x,y,z,0)\in\mathbb{R}^4:x^4+y^2+z^2=1\}$ diffeomorphic to $S^2$?
Thanks. I'm curious, how did you compute $\pi^{-1}$?
Aug
10
revised Is $\{(x,y,z,0)\in\mathbb{R}^4:x^4+y^2+z^2=1\}$ diffeomorphic to $S^2$?
added 46 characters in body
Aug
10
comment Is $\{(x,y,z,0)\in\mathbb{R}^4:x^4+y^2+z^2=1\}$ diffeomorphic to $S^2$?
@MichaelAlbanese Ok thanks, I will do that.
Aug
10
revised Is $\{(x,y,z,0)\in\mathbb{R}^4:x^4+y^2+z^2=1\}$ diffeomorphic to $S^2$?
added 219 characters in body
Aug
10
asked Is $\{(x,y,z,0)\in\mathbb{R}^4:x^4+y^2+z^2=1\}$ diffeomorphic to $S^2$?
Aug
10
accepted $\mathbb{Q}[X,Y]/(X^2+Y^2-1)$ is integrally closed
Jul
2
awarded  Curious
Apr
9
asked $\mathbb{Q}[X,Y]/(X^2+Y^2-1)$ is integrally closed
Apr
8
comment Why is $\mathbb{Q}[X,Y]/(X^2+Y^2-1)$ a Dedekind domain?
Thanks Hurkyl!${}$