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answered Describe $Spec( \mathbb C[x,y]/x(x-a))$ where $a$ is some complex number.
Aug
25
revised For a prime integer $p \in \{2, 3, 5, \cdots\}$, is $pR$ a maximal ideal in $R$?
typo
Aug
25
answered What is the intersection of the Segre variety in $\mathbb{P}^5$ and the Veronese surface in $\mathbb{P}^5$?
Aug
23
revised Divisors of zero in polynomial ring
added 146 characters in body
Aug
23
answered Divisors of zero in polynomial ring
Aug
20
comment Volume forms and volume of a smooth manifold
So you define $\int_M 1$ as $\int_M \omega$?
Aug
20
comment Volume forms and volume of a smooth manifold
What do you mean by $\int_M 1$? It does not make sense.
Aug
5
comment What does scheme with an action mean?
Have you hear about group actions in general?
Jul
29
answered Smooth Fano Polytopes and Hypersurfaces
Jul
28
comment Smooth Fano Polytopes and Hypersurfaces
You mean computing the Hodge numbers within M2? I would rather do that in Sage (which uses the formula you refer to).
Jul
28
comment Smooth Fano Polytopes and Hypersurfaces
Can you show the Macaulay2 code? One mistake I always do is that I use the wrong polytope when I should use the polar polytope instead. Computing Hodge numbers in M2 with equations is usually hopeless. First you have to find equations for your toric variety, and then add a "random" hyperplane equation. This greatly messes up the complexity of the Gröbner basis, so almost any computation with these equations are bound to take a looong time.
Jul
28
comment Open subscheme in special fiber
Well, the special fiber is a closed subscheme of $X$, and since opens are always dense, they cannot be contained in closed subschemes.
Jul
27
comment For any $A, B \in SL(2, F)$, does knowing $\operatorname{tr}A$, $\operatorname{tr}B$, and $\operatorname{tr}AB$ specify $A$ and $B$?
The conditions give you 5 equations and you have 8 unknowns. So no, you cannot determine the matrices unless you know more.
Jul
25
reviewed Approve Is direct limit of local rings a local ring?
Jul
22
awarded  Enlightened
Jul
21
awarded  Nice Answer
Jul
4
comment Finding the Krull dimension of a quotient ring $\mathbb{C}[x,y,z]/I$
@JohnnyT. Yes! .
Jul
4
answered Finding the Krull dimension of a quotient ring $\mathbb{C}[x,y,z]/I$
Jul
3
comment Lie bracket and flows on manifold
@Alfred I'd also like to see a geometric explanation, but I also believe that sometimes you just have to compute. You can draw pictures to see why something is approximately true, but to get exact formulas, you should sweat a bit.
Jul
3
comment Lie bracket and flows on manifold
@James Thank you for the comment. So there might perhaps be another way to show this that does use the chain rule?