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visits member for 2 years, 8 months
seen Jun 11 at 14:26

Jul
2
awarded  Curious
Jul
2
awarded  Inquisitive
Jun
6
comment Why are function fields of $U\subset V$ are equal?
@ZhenLin, could you give me a proof or a reference?
Jun
5
asked Why are function fields of $U\subset V$ are equal?
Jun
5
accepted Maps between tangent space of $X=\mathbb{V}(x^3-y^2)$ and $Y=\mathbb{V}(x^4-y^3)$
Jun
5
comment Maps between tangent space of $X=\mathbb{V}(x^3-y^2)$ and $Y=\mathbb{V}(x^4-y^3)$
@karl_christ, thanks! I will study your answer!
Jun
5
comment Maps between tangent space of $X=\mathbb{V}(x^3-y^2)$ and $Y=\mathbb{V}(x^4-y^3)$
@karl_christ, thats all right:) then could you help me check this exercise? Particularly the 3rd question.
Jun
5
comment Maps between tangent space of $X=\mathbb{V}(x^3-y^2)$ and $Y=\mathbb{V}(x^4-y^3)$
@karl_christ, isn't it common in algebraic geometry? Given a variety $X=\mathbb{V}(F_1,\cdots,F_r)$, then the tangent space of $X$ at $p$ is the variety $\mathbb{V}(d_pF_1,\cdots,d_pF_r)$ where $d_pF$ is the taylor expansion of $F$ to the first order.
Jun
5
asked Maps between tangent space of $X=\mathbb{V}(x^3-y^2)$ and $Y=\mathbb{V}(x^4-y^3)$
Jun
5
accepted What is the minimal depth of a decision tree if it grows to full size?
Jun
1
asked What is the minimal depth of a decision tree if it grows to full size?
May
30
asked Equivalent definitions of Jacobson rings
May
30
accepted What is the union of two varieties
May
29
comment Prove the strong Nullstellensatz from these two conditions
@GeorgesElencwajg, thanks! I have to say I might post a bad question. Indeed I am not sure the meaning of this exercise. Anyway, your answer helps a lot:)
May
29
asked What is the union of two varieties
May
29
comment Prove the strong Nullstellensatz from these two conditions
@adrido, yes I know we can prove (1) and (2) independently. But I guess the target of the exercise is to let you prove the Nullstellensatz with only the knowledge given in (1) and (2)...
May
28
asked Prove the strong Nullstellensatz from these two conditions
May
28
comment Calculate $\mathcal{O}_{X,p}$ for $X=\mathbb{V}(xy)\subset\mathbb{A}^2$
@FredrikMeyer,clear now, thanks!
May
28
comment Calculate $\mathcal{O}_{X,p}$ for $X=\mathbb{V}(xy)\subset\mathbb{A}^2$
@FredrikMeyer, hi, I still have some confusion. In the second case, are you suggesting the local ring is isomorphic to $k[x]$ localized at $(x)$? Why can we change from localizing at $(x, y-1)$ to at $(x)$? You said since we can divide by $y$, it becomes a unit, which I think implies $(xy)=(x)$, so the coordinate ring $k[x,y]/(xy)$ becomes $k[x,y]/(x)$. But how does this affect the ring at which we are localizing, i.e. $(x, y-1)$? What about that we can divide by $y+1, y-3$, etc?
May
28
accepted Calculate $\mathcal{O}_{X,p}$ for $X=\mathbb{V}(xy)\subset\mathbb{A}^2$