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May
19
awarded  Nice Answer
May
19
comment Dimension of affine part equals to the dimension of the variety
The dimension of $\mathbb P^n$ is not equal to the Krull dimension of its projective coordinate ring $k[x_0,\ldots,x_n]$, which is $n+1$. That's because $\mathbb P^n$ is not an affine variety. The problem with your question is that it is ill-posed: What is your definition of the dimension of $\mathbb P^n$?
May
18
comment Inclusion of Tori induces surjection of character groups?
This is true, but I have too little time for anything but a reference right now: Tauvel & Yu, Lie algebras and algebraic groups, 22.5.4 (iii) is a slightly more general statement for diagonalizable algebraic groups. Any torus is diagonalizable, of course.
May
12
comment Inclusionwise maximal linear subvarieties of a projective variety
@DanielMcLaury: Interesting, I didn't see that angle. If I am not somehow mistaken, this is the image of a projective morphism, so it should be closed. Any flaws in that argument?
May
12
asked Inclusionwise maximal linear subvarieties of a projective variety
May
10
accepted Is every codimension one subvariety of a projective variety a set-theoretic complete intersection?
May
10
revised Is every codimension one subvariety of a projective variety a set-theoretic complete intersection?
added 639 characters in body; edited tags
May
10
asked Is every codimension one subvariety of a projective variety a set-theoretic complete intersection?
May
6
comment what is the precise definition of a morphism defined over $k$?
@ZhenLin: That's true, but along with your comment above this should be enough for the OP, I hope.
May
5
answered what is the precise definition of a morphism defined over $k$?
May
4
comment A confusion on the definition of morphism between varieties
I believe the answer to your question might be Lemma I.3.6 in Hartshorne.
Apr
23
answered Number of inflection points of an algebraic projective curve
Apr
22
answered Are points in general position generic points?
Apr
22
comment Every variety contains open affine normal subvariety
@DanielMcLaury: Good point, fixed.
Apr
22
revised Every variety contains open affine normal subvariety
added 13 characters in body
Apr
21
revised $\Bbb K$-algebra structure on isomorphic vector space
deleted 14 characters in body; edited title
Apr
21
answered Every variety contains open affine normal subvariety
Apr
21
revised Is the preimage of the non-normal locus a divisor?
edited tags
Apr
21
comment Is the preimage of the non-normal locus a divisor?
@AsalBeagDubh: A very good nitpick, I fixed that.
Apr
21
revised Is the preimage of the non-normal locus a divisor?
deleted 37 characters in body