1,254 reputation
1520
bio website n/a
location Berlin, Germany
age 27
visits member for 2 years, 7 months
seen 5 hours ago

Currently a PhD student at HU Berlin. I'm interested in the geometry of moduli spaces of curves.


Nov
22
comment Is every complex (smooth) manifold a scheme?
Actually, if you want $X^{\text{an}}$ to be a smooth manifold, $X$ needs to be a smooth variety. I have never seen the analytification functor for something else than schemes of finite type over $\mathbb{C}$.
Jul
29
comment Is this really a typo?
If a function $f$ is $C^k$ for $k\geq 1$ then it automatically is $C^1$, too. So the statement is valid.
Jul
4
comment Algebraic Solutions to Systems of Polynomial Equations
By 'all variables algebraic' you mean one solution will be a tuple of algebraic numbers?
Jun
28
comment An affine open neighborhood of a nonsingular point
No, it is not. In fact, it is a rich source of counterexamples regarding schemes that are not varieties.
Jun
27
comment An affine open neighborhood of a nonsingular point
Your $\Gamma(U,\mathcal{O}_X)$ is (by definition of finite type) a finitely generated $k$-algebra, not just a localization of one.
Jun
10
comment My sister absolutely refuses to learn math
I tend to agree with your last sentences but it is not at all clear to me whether quick learning later on is not actually also a function of having spent large amounts of time in school on the subject.
Jun
3
comment Theorems' names that don't credit the right people
Which is not at all wrong since the circumflex just denotes a left-out 's' from old French spelling.
Dec
20
comment Find all polynomials that fix $\mathbb Q$ and the irrationals
For instance, $x^2$ will map $\sqrt{2}$ to $2$, and therefore be a counterexample.
Dec
19
comment Difference between a stalk of a sheaf and a fiber of a vector bundle
No need to be sorry. Next to each answer, under the arrows for up/downvoting, there is a little check mark. You can just click on the check mark belonging to the answer you like best to accept it. See here for some images explaining the process.
Dec
19
comment Difference between a stalk of a sheaf and a fiber of a vector bundle
Please consider accepting some answers to your previous questions. People will be less willing to respond if they think you won't appreciate their answers anyway.
Dec
16
comment Normality in a group $G$
Please supply some additional information, so that we can help you better. What have you done? Where are you stuck?
Dec
13
comment Is $R = Q[x] / (x^4 - 3x^2+ 6x)$ isomorphic to a direct sum of two fields?
We would appreciate it to see some thoughts of your own on this. Also, it is a bit rude to command us to prove it.
Dec
12
comment Let $G_1. …, G_k$ be any groups and $\sigma \in S_k$ a permutation. Prove the following map defines an isomorphism
Think about the inverse of the permutation.
Dec
5
comment Is it true that if a graph is n-regular that it must have n+1 vertices?
I interpreted that as 'exactly', but you're right, maybe it was meant as 'at least'. Curiously, I didn't consider this, even if I used to draw two cards when someone told me to "Draw one card".
Dec
5
comment Is it true that if a graph is n-regular that it must have n+1 vertices?
No, it's not true. Google images for "3-regular graph" shows many counterexamples. A very famous one is the Petersen graph.
Dec
4
comment Is $\mathbb R^2$ a field?
Indeed, every finite-dimensional vector space $V$ over a field $\mathbb{F}$ is isomorphic to $\mathbb{F}^n$, where $n$ is the dimension of $V$. This fact impressed me a lot when I first learned it.
Dec
3
comment Conceptual question about equivalence of eigenvectors
Yes. The eigenvalue doesn't even need to be $1$.
Dec
2
comment Proving that an equation has no natural solutions
Wow, this is really clever!
Nov
30
comment A set of objects that satisfy $a^2 = \alpha x$ and commute
Did you mean to write "with generators $\{x\}\cup Y$"?
Nov
30
comment Are CASs useful in mathematics?
Sage has become a very good choice for many problems, being sometimes faster than all other packages. But it has neither the stability of Magma, nor the user-friendly functionality of, e.g., Mathematica. This may change in some years, of course.