Jesko Hüttenhain
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Registered User
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PhD Student in Paderborn, Germany.
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May 8 |
asked | Expression of basis vectors of permutation modules in different bases. |
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May 8 |
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A basis of the symmetric power consisting of powers Hey! 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. |
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May 8 |
revised |
A basis of the symmetric power consisting of powers added 8 characters in body |
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Apr 24 |
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The notion of multiplicity in algebraic geometry Thanks 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. |
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Apr 23 |
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The notion of multiplicity in algebraic geometry Your 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 $f\in m^i$. |
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Apr 23 |
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The notion of multiplicity in algebraic geometry I 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! |
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Apr 23 |
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The notion of multiplicity in algebraic geometry Not 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? |
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Apr 22 |
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The notion of multiplicity in algebraic geometry Yea, 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. |
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Apr 22 |
asked | The notion of multiplicity in algebraic geometry |
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Apr 17 |
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A basis of the symmetric power consisting of powers Oh, 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. |
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Apr 17 |
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A basis of the symmetric power consisting of powers That'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. |
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Apr 17 |
asked | A basis of the symmetric power consisting of powers |
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Apr 11 |
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Syzygies of determinantal varieties: Looking for English text Thanks a lot, this does indeed look very helpful. |
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Apr 10 |
answered | Syzygies of determinantal varieties: Looking for English text |
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Apr 10 |
asked | Syzygies of determinantal varieties: Looking for English text |
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Apr 10 |
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The shortest mathematical paper @Michael: Done and thanks, that thread's got some great examples. |
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Apr 10 |
asked | The shortest mathematical paper |
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Apr 4 |
asked | The Hilbert function of an intersection |
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Mar 26 |
awarded | ● Nice Question |
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Mar 1 |
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Decomposition of $\mathrm{End}(V)$ as $S_n\times S_n$-module It 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. |
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Feb 28 |
asked | Decomposition of $\mathrm{End}(V)$ as $S_n\times S_n$-module |
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Feb 15 |
awarded | ● Enthusiast |
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Feb 10 |
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Question about local description of the branch locus A 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 =). |
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Feb 5 |
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Question about local description of the branch locus added 192 characters in body |
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Feb 5 |
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Question about local description of the branch locus This 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 =). |
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Jan 29 |
asked | Question about local description of the branch locus |
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Jan 22 |
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Top chern class under finite, unramified, dominant morphism PS: I ask because that corollary is, in fact, of serious interest to me =). |
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Jan 22 |
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Top chern class under finite, unramified, dominant morphism First 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? |
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Jan 20 |
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Top chern class under finite, unramified, dominant morphism Out of curiosity, though: Is there a "direct" proof for this equality, without identifying $c_n$ with the Euler characteristic? |
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Jan 20 |
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Top chern class under finite, unramified, dominant morphism Precisely what I had hoped for. Looking back now, I should have searched for "étale cover". Thanks a lot! |
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Jan 20 |
asked | Top chern class under finite, unramified, dominant morphism |
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Jan 17 |
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Higher dimensional version of the Hurwitz formula? That was truly enlightening. Thanks a bunch. |
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Dec 13 |
awarded | ● Organizer |
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Dec 1 |
awarded | ● Nice Answer |
