480 reputation
310
bio website
location
age
visits member for 2 years, 5 months
seen Aug 11 at 5:46

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!${}$
Apr
8
comment Why is $\mathbb{Q}[X,Y]/(X^2+Y^2-1)$ a Dedekind domain?
@user26857 May I ask how? I guess I don't know the method.
Apr
8
revised Why is $\mathbb{Q}[X,Y]/(X^2+Y^2-1)$ a Dedekind domain?
added 4 characters in body
Apr
8
comment Why is $\mathbb{Q}[X,Y]/(X^2+Y^2-1)$ a Dedekind domain?
Thanks, I'll look into this in the future.
Apr
8
comment Why is $\mathbb{Q}[X,Y]/(X^2+Y^2-1)$ a Dedekind domain?
In that case, do you have a reference for where it is proven that Dedekind rings arise as the coordinate rings of smooth affine curves? I've been googling around, but haven't found it.
Apr
7
comment Why is $\mathbb{Q}[X,Y]/(X^2+Y^2-1)$ a Dedekind domain?
Thanks Georges. I was hoping to see an algebraic proof, since I've studied algebra, but not geometry in any satisfactory sense, so I'd have a better chance of understanding an algebraic answer. I've no doubt your answer is elegant and correct, but "a smooth affine curve has as coordinate ring a Dedekind ring" makes little sense to me.
Apr
7
asked Why is $\mathbb{Q}[X,Y]/(X^2+Y^2-1)$ a Dedekind domain?
Mar
23
awarded  Yearling
Feb
12
accepted If $N\cap rM=rN$ for all $r\in R$, then is $M=N\oplus K$ for some $K$?