# Jesko HÃ¼ttenhain

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## Registered User

 Name Jesko HÃ¼ttenhain Member for 2 years Seen 18 hours ago Website Location Germany Age 27
 May8 asked Expression of basis vectors of permutation modules in different bases. May8 comment A basis of the symmetric power consisting of powersHey! This sounds like a really great approach, but I must confess I do not see (at all) how the formula in Theorem 9.6.1 implies the claim that all the $(\sum_i \alpha_i x_i)^k$ form a basis of the degree-$k$ polynomials. Would you mind giving a little more detail? I would really appreciate it. May8 revised A basis of the symmetric power consisting of powersadded 8 characters in body Apr24 comment The notion of multiplicity in algebraic geometryThanks a bunch. I accepted this answer because it helps me most for what I am doing, but thanks to Filippo Edoardo and Will Savin for the very helpful explanations. Apr23 comment The notion of multiplicity in algebraic geometryYour definition of $\mathrm{ord}(f)$ confuses me because for one thing, it does not depend on $f$ at all and second, $I\in m^i$ looks a lot like you ment to write $f\in m^i$. Apr23 comment The notion of multiplicity in algebraic geometryI suppose $\mathrm{ord}(f)=\sup\{ i\mid f\in m^i \}$, yes? So basically, I can use my definition in the case where $X$ is a regular scheme, which might just be good enough for me. +1 and thanks! Apr23 comment The notion of multiplicity in algebraic geometryNot that it really matters, but I thought $3$ sounded reasonable: We have the ring $k[t^2,t^3]/(t^4)=k[x,y]/(x^2,x^3-y^2)$ where $x=t^2$, $y=t^3$ and $xy=t^5$. One more question, though: You say that the Definitions agree when the local ring is a DVR: Do you have a reference? Apr22 comment The notion of multiplicity in algebraic geometryYea, that was exactly my suspicion. I would like to know how (or rather when) it misbehaves, though - most of the time I am dealing with very forgiving kinds of schemes anyway. Apr22 asked The notion of multiplicity in algebraic geometry Apr17 comment A basis of the symmetric power consisting of powersOh, don't get me wrong, these elements were my first choice as well and I very much believe that they work, but I can't prove it. Apr17 comment A basis of the symmetric power consisting of powersThat's basically the elements from the proof I referenced, but for $k>2$ it requires more than $\binom{n+k-1}k$ terms, namely all the $(x_{i_1}+\cdots+x_{i_j})^k$ for $2\le j\le k$. It's not obvious to me why only the ones for $j=k$ should suffice. Apr17 asked A basis of the symmetric power consisting of powers Apr11 comment Syzygies of determinantal varieties: Looking for English textThanks a lot, this does indeed look very helpful. Apr10 answered Syzygies of determinantal varieties: Looking for English text Apr10 asked Syzygies of determinantal varieties: Looking for English text Apr10 comment The shortest mathematical paper@Michael: Done and thanks, that thread's got some great examples. Apr10 asked The shortest mathematical paper Apr4 asked The Hilbert function of an intersection Mar26 awarded ● Nice Question Mar1 comment Decomposition of $\mathrm{End}(V)$ as $S_n\times S_n$-moduleIt is a start, indeed, but I don't really know how to compute $\langle s_\lambda, s_\mu[h]\rangle$ either. In fact, I haven't even fully understood Stanley's definition of plethysm, but maybe I have a better chance after reading the Appendix from the start. Feb28 asked Decomposition of $\mathrm{End}(V)$ as $S_n\times S_n$-module Feb15 awarded ● Enthusiast Feb10 comment Question about local description of the branch locusA personal matter came up and I missed the deadline for assigning the bounty, though I certainly would have done so. I even sent a mail to the moderators, but apparently this mistake is irreversible. I hope my heartfelt thanks are enough then =). Feb5 revised Question about local description of the branch locusadded 192 characters in body Feb5 comment Question about local description of the branch locusThis is exactly what I am asking. I should have added that I assume $n$ not divisible by $\mathrm{char}(\Bbbk)$ and of course, yea, I assume the $x_i$ reduced and coprime. I was pretty sure that this is true, but I wanted confirmation. To be honest, I don't perfectly understand your argument, though: Can I somehow argue that $Y$ locally looks like a fiber product? What exactly do you mean by $nT_1^{n-1}=0$, you kinda took the derivative there? I'm sorry, I just don't perfectly understand. Anyhow, it's precisely what I want and if you can elaborate, you very much deserve the bounty =). Jan29 asked Question about local description of the branch locus Jan22 comment Top chern class under finite, unramified, dominant morphismPS: I ask because that corollary is, in fact, of serious interest to me =). Jan22 comment Top chern class under finite, unramified, dominant morphismFirst of all, +1 and thanks for the very detailed Answer. I only know Mayer-Vietoris for singular Homology, is there an equivalent for the $\ell$-adic one? Jan20 comment Top chern class under finite, unramified, dominant morphismOut of curiosity, though: Is there a "direct" proof for this equality, without identifying $c_n$ with the Euler characteristic? Jan20 comment Top chern class under finite, unramified, dominant morphismPrecisely what I had hoped for. Looking back now, I should have searched for "étale cover". Thanks a lot! Jan20 asked Top chern class under finite, unramified, dominant morphism Jan17 comment Higher dimensional version of the Hurwitz formula?That was truly enlightening. Thanks a bunch. Dec13 awarded ● Organizer Dec1 awarded ● Nice Answer