3,605 reputation
831
bio website nullteilerfrei.de
location Germany
age 29
visits member for 3 years, 1 month
seen yesterday

I'm a PhD student with research interests in Algebraic Geometry, Algebraic Complexity Theory and Geometric Invariant Theory.


Jul
8
comment Integral dependence of coordinate ring
I don't think he shows that. First, $S(Y)_{(x_i)}$ does not properly contain $S(Y)$ and it is not clear how $S(Y)$ should act (by scalar multiplication) on $S(Y)_{(x_i)}$. Observe that the latter are only the fractions in degree zero! Second, the ring $S(Y)_{x_i}$ is a good example of an extension of $S(Y)$ which is not integral. Intuitively, this is because you added a new fraction, which is against the spirit of remaining integral. I can also write a formal proof if you like.
Jun
26
comment Two nonassociated functions defining the same hypersurface?
Indeed, this works! Thanks!
Jun
9
comment What are the one-parameter subgroups of GL?
Nice! The density argument is really elegant, also thanks for answering such an old question.
Jun
3
comment Two nonassociated functions defining the same hypersurface?
It does work, but I realized what bothers me about it and slightly changed my question: The variety $X$ is not irreducible in this case and I am wondering if it will still hold under that condition.
Jun
3
comment Two nonassociated functions defining the same hypersurface?
This yields an affine example, which is already nice: Take the Neil Parabola with coordinate ring $\mathbb C[x,y]/(x^2-y^3)$ and the functions $g=x$ and $f=y$. They both define the same point, they are not associated and irreducible. And you are right, it is because they are both not prime, the minimal prime ideal over both of them is $(x,y)$. However, this argument does not work well after homogenization to $\mathbb C[x,y,z]/(zx^2-y^3)$. Any ideas? Is the projective case different or am I looking at the wrong example?
May
27
comment How to find the lengths of the shortest paths in a directed graph in $O(m)$ steps?
You're right, but now that I think about it we have to be more specific. Do you want the lengths of all shortest paths for all pairs of vertices? In this case, you need $\mathcal O(n^2)$ steps anyway, because you have quadraticly many values to compute.
May
26
comment How to find the lengths of the shortest paths in a directed graph in $O(m)$ steps?
I think you can simply use BFS.
May
21
comment Differentials on a curve
Is $G$ finite? Or is it an algebraic group? In general, it is not clear how $C/G$ has the structure of a variety.
Apr
23
comment Ring of Formal Power Series Over a Field is a Local Ring
@fretty: +1 for "everyday power series".
Apr
19
comment Kid's homework: 4 equations 5 unknowns? Going crazy!
There is no unique solution to that system of equations even if you limit yourself only to the natural numbers. I am posting just to confirm your observation, but concur with @naslundx.
Apr
8
comment Do rational functions separate points?
@Cantlog: That's really great and a clear, elegant proof at that. Why don't you post it as an answer, I'd accept in a heartbeat.
Apr
7
comment Do rational functions separate points?
@AsalBeagDubh: Well. I wanted to avoid it, but if you have a solution for quasi-projective $X$, I'd be curious, too.
Apr
6
comment How to determine the local ring
It means localization in the multiplicative set $\{ x^k \mid k\in\mathbb N\}$. It is sometimes referred to as localization in $x$. It means adjoining $x^{-1}$, basically. Also, don't worry about questions ;).
Apr
6
comment How to determine the local ring
Yes, that is what I mean.
Apr
5
comment How to determine the local ring
In larger generality, when $X$ is normal and $Z\subseteq X$ is of codimension greater or equal than two, then $\mathcal O(X)=\mathcal O(X\setminus Z)$. In this concrete case, it means that any regular function on $A^2\setminus\{ 0 \}$ can be extended to a polynomial on $A^2$. Indeed, interpret that function as a rational function $f/g$ - there is no way that $g$ only vanishes at a single point, it would have to vanish at a codimension one subvariety. Hence, the function must be a polynomial.
Apr
5
comment Image of Regular Map
I am reasonably sure he means the affine plane over a field.
Apr
3
comment Proving $\mathscr L(C_G(H)) \subseteq \mathfrak c_{\mathfrak g}(\mathfrak h) = \{ \mathrm x \in \mathfrak g \mid [\mathrm x, \mathfrak h] = 0\}$
I gave this answer recently, it seems like the same question.
Mar
27
comment Placing n points in a MxM square grid
Are you required to do this "on-line", as in the paper? Be aware that this means the following: Your algorithm does not know how many points have to be placed before it runs! This makes the whole thing much more difficult than in the case where the algorithm knows how many points have to be placed from the beginning.
Mar
11
comment Orthogonal invariants of an irredubile GL-representation
As a second comment, do you have some references for this branching rule? That'd be really great. Thanks so much already, though!
Mar
11
comment Orthogonal invariants of an irredubile GL-representation
The partition corresponding to the invariants should be $(0)$, not $(1)$ - that'd mean that it's the case if $\lambda$ has only even summands, right?