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May
21
revised Zeroes of prime polynomials in the algebraic torus (A Hilbert's Nullstellensatz for Laurent polynomials?)
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May
21
comment Zeroes of prime polynomials in the algebraic torus (A Hilbert's Nullstellensatz for Laurent polynomials?)
You are, of course, completely correct. Regarding your second thing, I missed the "different" ... so yea, you are right about that, too.
May
21
answered Zeroes of prime polynomials in the algebraic torus (A Hilbert's Nullstellensatz for Laurent polynomials?)
May
20
comment Can someone illustrate the definition of manifold with a simple example?
The most classical example would be the sphere in $\mathbb R^3$. For any point $x$, you can pick the point opposite to it $y$ and use the stereographic projection map to identify $M\setminus\{y\}$ with $\mathbb R^2$.
May
19
awarded  Enlightened
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?
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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
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