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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?
Jul
3
answered Lie bracket and flows on manifold
Jul
3
comment Why is the sheaf $\mathcal{O}_X(n)$ called the “twisting sheaf” (where $X=\operatorname{Proj}(S)$ for a graded ring $S$)?
@MarianoSuárez-Alvarez: Could you explain how $\mathscr O(1)$ is a Möbius band (or provide a link)? I'm not sure if I see the connection.
Jun
29
comment how much differential structure can we put on countable manifolds?
Homeomorphic to $\mathbb Q^n$ in which topology?
Jun
26
answered Is the total space of a vector bundle over an irreducible scheme irreducible?
Jun
23
revised Singular plane cubic curve birational to $\mathbb{P}^1$
added 1 character in body
Jun
23
answered Finite Variety in $\mathbb{C}^5$
Jun
22
answered Example: Krull dimension 1 but not a PID
Jun
19
comment On projection $\mathbb{P}_A^n \rightarrow \mathbb{P}_A^{n-1}$
@user249180 The point [0,..,0,1] corresponds to the prime ideal $(x_0,\ldots,x_{n-1})$.