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Mar
16
comment An isomorphism from $GL_{2}(\mathbb{F_{2}})$ to $S_{3}$
These two groups are not isomorphic. $\operatorname{GL}_3(\mathbb F_2)$ has at least $7$ elements, because there are $7$ nonzero vectors in $\mathbb F_2^3$. On the other hand, $S_3$ only contains $6$ elements.
Mar
16
answered Looking for a proof that the resultant is the product of the differences of roots
Mar
13
accepted Do rational functions separate points?
Mar
13
awarded  Nice Answer
Mar
12
awarded  Revival
Mar
12
revised $\mathbb{G}_a$ or $\mathbb{G}_m$ as subgroups of Affine Algebraic Groups
added 8 characters in body
Mar
12
answered $\mathbb{G}_a$ or $\mathbb{G}_m$ as subgroups of Affine Algebraic Groups
Mar
12
answered Prove that for each $p \in Y$ the quotient field of $O_p$ is isomorphic to the field $K(Y)$.
Mar
11
comment Resolution of singularities of the determinant hypersurface
This is indeed a very nice resolution. I would have preferred an embedded one, but this is quite a nice start, so +1 and accept. Thanks!
Mar
11
accepted Resolution of singularities of the determinant hypersurface
Mar
11
comment Can a birational morphism surject from an affine to a projective variety?
+1 and accept, also thank you, this is a nice proof.
Mar
11
accepted Can a birational morphism surject from an affine to a projective variety?
Mar
10
answered The 2 Charts of “Blowing up the Origin in $\mathbb{C}^2$ ”
Mar
7
answered why are projective spaces and varieties prefferable?
Mar
7
comment True or False: $f$ is injective if and only if $f^*$ is surjective where $f^*$ is corresponding to the pullback to $f$.
Of course, you can easily turn this into a direct proof, which is then more elegant. But it is late, and I will leave you with this.
Mar
7
answered True or False: $f$ is injective if and only if $f^*$ is surjective where $f^*$ is corresponding to the pullback to $f$.
Mar
6
comment Can a birational morphism surject from an affine to a projective variety?
@AlexYoucis: What is the argument for the fact that it has an inverse on some $U\subseteq Y$ whose complement is codim. 2? The approach sounds interesting!
Mar
4
comment Can a birational morphism surject from an affine to a projective variety?
@karl_christ: No, I mean surjective. Every fiber is nonempty.
Mar
4
comment Can a birational morphism surject from an affine to a projective variety?
@karl_christ: Such a map would only give me an isomorphism of a dense open subset $U\subseteq X$ with another dense open subset $V\subseteq Y$ of $Y$. This proves nothing.
Mar
4
comment Can a birational morphism surject from an affine to a projective variety?
@KReiser: Yea, I edited my question, this only makes sense for irreducible varieties.