# Tagged Questions

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### intersection multiplicity at non-zero point

Compute the intersection multiplicity of $f=x+y-2$ and $g=x^2+y^2-2$ at $(1,1)$. Is this the same as the intersection multiplicity of $f(x+1)$ and $g(x+1)$ at $(0,0)$ which I have computed to be 2? ...
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### Computing irreducible components of algebraic set

Consider the algebraic set $V(X^2-YZ,X-XZ)$. Find the irreducible components of this set and show that $I(V)=(X^2-YZ,X-XZ)$. I reasoned that $X-XZ=0$ iff $X=0$ or $Z=1$. If $X=0$, we get $Y=0$ or ...
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### Find intersection multiplicities

Let curves $A$ and $B$ be defined by $x^2-3x+y^2=0$ and $x^2-6x+10y^2=0$. Find the intersection multiplicities of all points of intersection of $A$ and $B$. If we let $f=x^2-3x+y^2$ and ...
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### Example: Irreducible component - affine varieties

Again, I know how to prove the statement. But, I cannot find any example. Please help me for finding an example. Thank you:)
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### Affine variety example.

I know how to show the statement. But I cannot find an example (the part I underlined by a yellow pen) please help me for finding an example. Note: For example, can I consider the following ...
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When reading about Quantum Mechanics, I always feel a bit disappointed when physicists consider that (for example) the 3-dimensional position of a particle must be decomposed into 3 coordinates $x, y, ... 1answer 122 views ### Find the tangent space of$\mathrm{Aff}(n)$Find the tangent space of$\mathrm{Aff}(n)$. see Proof: Tangent space of the general linear group is the set of all squared matrices$\mathrm{Aff}(n)$is the set of all matrices of the form$$... 1answer 102 views ### Finding a coset I'm given$V$a vector space over a field$\mathbb{F}$. Letting$v_1$and$v_2$be distinct elements of$V$, define the set$L\subseteq V$:$L=\{rv_1+sv_2 | r,s\in \mathbb{F}, r+s=1\}$. (This is the ... 1answer 111 views ### Affine Subspace Confusion I'm having some trouble deciphering the wording of a problem. I'm given$V$a vector space over a field$\mathbb{F}$. Letting$v_1$and$v_2$be distinct elements of$V$, define the set$L\subseteq ...
I'm looking for an example of $n$-dimensional affine space that is isomorphic with $\mathbb{R}^n$ as affine space but not with respect to other properties (for example it has different ordering etc.) ...
What are some examples of this? Say for $F_{4}$. I know this is a very simple question, but I can't find any info on it. Edit: Yes, I was thinking of $F_{2}[x]/(x^2+x+1)$. I was confused.