most recent 30 from http://mathoverflow.net 2013-05-19T19:38:43Z http://mathoverflow.net/feeds/user/1992 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/111400/good-computer-package-for-calculating-inverse-of-a-formal-power-series minimax 2012-11-03T19:03:01Z 2013-05-10T14:00:07Z

<p>Hello Everyone,</p> <p>This might be a question people already asked or is obvious to experts, or is not appropriate for this forum, if so, I apologize. I am trying to calculate things like $z/(e^z-1)$, or find the inverse of $x=z+ 2z+5z^2+\cdots$, expand as power series. What is the best (or favorite) software package you use to do stuff like this?</p> <p>Thanks in advance!</p>

http://mathoverflow.net/questions/123696/algorithm-for-computing-basis-of-zero-dimensional-ring minimax 2013-03-06T02:49:05Z 2013-03-06T06:40:16Z

<p>If given a zero dimensional ring over a field, for example, a polynomial ring $A=k[x_1,\ldots,x_n]/(f_1,\ldots,f_n)$ such that $A$ is 0-dimensional, is there an algorithm to compute a monomial basis for this ring?</p>

http://mathoverflow.net/questions/122359/computer-package-to-compute-homfly-polynomial minimax 2013-02-19T22:49:40Z 2013-02-19T22:49:40Z

<p>I apologize of already asked by someone else, but what (in your opinion) is the best package for computing HOMFLY polynomials?</p>

http://mathoverflow.net/questions/119140/what-are-the-general-techniques-for-proving-a-variety-is-not-toric minimax 2013-01-17T06:31:56Z 2013-01-19T00:54:26Z

<p>When I read the paper "A survey on Cox rings" with the link below:</p> <p><a href="http://math.berkeley.edu/~velasco/Survey.pdf" rel="nofollow">http://math.berkeley.edu/~velasco/Survey.pdf</a></p> <p>In Section 4.2 it is mentioned that the Del Pezzo surface given by blowup of $\mathbb{P}^2$ at $s>3$ general points is not toric. Is there an easy way to see this?</p>

http://mathoverflow.net/questions/112308/cell-decomposition-of-punctual-hilbert-scheme-of-points-on-an minimax 2012-11-13T18:51:28Z 2012-12-31T07:28:09Z

<p>Hello Everyone,</p> <p>I am thinking on calculating the motive of Hilbert scheme of points on a smooth variety, of any dimension. There is a famous paper by Gottsche that calculates the Hilbert scheme of points on a smooth surface, which uses a cell decomposition of punctual Hilbert scheme of points on the plane. I am wondering if a similar results hold for punctual Hilbert scheme of any dimension, or at least is it known that such cell decomposition exists?</p> <p>I apologize if this is a stupid question.</p> <p>Best, minimax</p>

http://mathoverflow.net/questions/113866/how-fine-one-must-choose-an-affine-cover-to-get-weil-restriction minimax 2012-11-19T20:24:49Z 2012-11-20T02:22:11Z

<p>Hello Everyone,</p> <p>It is well-known that Weil restriction does not commute with the formation of affine open covers, so I am wondering how fine one must choose an affine cover to recover the Weil restriction. More precisely, let $L/K$ be a finite separable extension, $X$ be a variety over $L$. Let ${U_i}$ be an affine open cover of $X$. For each $i$, one can Weil restrict to get the Weil restriction $V_i$ which is a variety over $K$. The gluing data for $U_i$ descends to gluing data for $V_i$ so we can glue the $V_i$'s together. But it is not true that for any open cover ${U_i}$, the $V_i$'s glue to get $R_{L/k}X$. So the question is, under what condition does those $V_i$'s glue to get $R_{L/K}X$?</p> <p>Upon reading the book Neron model, in particular the last paragraph of the proof of Theorem 4 on page 195, I thought that it is sufficient if any $d$ points of $X$ lie in some $U_i$, where $d=[L:K]$ is the degree of field extension (reason is that, for any $K$-scheme $T$, let $T'=T\times_KL$, then any fiber in the projection $T'\to T$ contains at most $d$ points, now follow the proof of that Theorem). Is this correct?</p> <p>Thanks! </p>

http://mathoverflow.net/questions/51494/why-the-name-separable-space minimax 2011-01-08T20:36:56Z 2011-08-09T01:23:30Z

<p>It is well known that a separable space is a topological space that has a countable dense subset. I am wondering how is this related to the name 'separable'? Any intuition where the name come from?</p>

http://mathoverflow.net/questions/55244/why-nilpotent-elements-must-be-allowed-in-modern-algebraic-geometry minimax 2011-02-12T22:16:37Z 2011-02-17T13:03:38Z

<p>On the Wikipedia page about algebraic varieties <a href="http://en.wikipedia.org/wiki/Algebraic_variety" rel="nofollow">http://en.wikipedia.org/wiki/Algebraic_variety</a>, a sentence reads as follows:</p> <p>[[A more significant modification is to allow nilpotents in the sheaf of rings. A nilpotent in a field must be 0: these if allowed in coordinate rings aren't seen as coordinate functions.</p> <p>From the categorical point of view, nilpotents must be allowed, in order to have finite limits of varieties (to get fiber products).]]</p> <p>So I am wondering if there is an intuitive example to get non-reduced 'schemes' from reduced 'algebraic varieties' (probably by taking fiber product or alike)? </p>

http://mathoverflow.net/questions/123696/algorithm-for-computing-basis-of-zero-dimensional-ring minimax 2013-03-06T06:41:44Z 2013-03-06T06:41:44Z

@Qiaochu: I just meant the global section of Spec of that ring, i.e. the ring itself.... It seems unnecessary to use that language so I have changed the working. Sorry for the confusion...

http://mathoverflow.net/questions/123696/algorithm-for-computing-basis-of-zero-dimensional-ring minimax 2013-03-06T04:29:05Z 2013-03-06T04:29:05Z

@Steven: I am curious what algorithm does that command use?

http://mathoverflow.net/questions/122359/computer-package-to-compute-homfly-polynomial minimax 2013-02-21T05:37:36Z 2013-02-21T05:37:36Z

@Steven: I have installed the package and it works nice! One more question, how to generate the cable over trefoil in that package?

http://mathoverflow.net/questions/122359/computer-package-to-compute-homfly-polynomial minimax 2013-02-21T04:10:41Z 2013-02-21T04:10:41Z

@Andrew: Thanks!

http://mathoverflow.net/questions/122359/computer-package-to-compute-homfly-polynomial minimax 2013-02-20T01:11:40Z 2013-02-20T01:11:40Z

@Steven: Thanks, I will try it out!

http://mathoverflow.net/questions/122359/computer-package-to-compute-homfly-polynomial minimax 2013-02-20T00:03:16Z 2013-02-20T00:03:16Z

@Ryan: I want to compute the HOMFLY polynomial of (3,19) cable over trefoil.

http://mathoverflow.net/questions/119140/what-are-the-general-techniques-for-proving-a-variety-is-not-toric minimax 2013-01-19T00:55:01Z 2013-01-19T00:55:01Z

@Piotr: Thanks, it has been changed!

http://mathoverflow.net/questions/119140/what-are-the-general-techniques-for-proving-a-variety-is-not-toric minimax 2013-01-17T07:05:36Z 2013-01-17T07:05:36Z

@Piotr: Changed!

http://mathoverflow.net/questions/63301/when-will-the-pushforward-of-a-structure-sheaf-still-be-a-structure-sheaf/63308#63308 minimax 2013-01-03T01:40:14Z 2013-01-03T01:40:14Z

Is the reference to Hartshorne III.10.3 correct?

http://mathoverflow.net/questions/113866/how-fine-one-must-choose-an-affine-cover-to-get-weil-restriction/113891#113891 minimax 2012-11-20T07:52:26Z 2012-11-20T07:52:26Z

@nosr: I think I figured this out, by infinitesimal criterion for etaleness: a morphism $f: X\to Y$ of locally of finite presentation iff for any $Y$-scheme $T$ and closed subscheme $T_0$ of $T$ defined by a square zero ideal, the map of sets $\Hom_Y(X,T)\to\Hom_Y(X,T_0)$ is bijective. Now etaleness follows if we use the universal property defining Weil restriction and the above criterion....

http://mathoverflow.net/questions/113866/how-fine-one-must-choose-an-affine-cover-to-get-weil-restriction/113891#113891 minimax 2012-11-20T05:02:30Z 2012-11-20T05:02:30Z

Excellent answer! A possible dumb question: why is Weil restriction of an open immersion etale?

http://mathoverflow.net/questions/112308/cell-decomposition-of-punctual-hilbert-scheme-of-points-on-an minimax 2012-11-13T20:11:31Z 2012-11-13T20:11:31Z

@Dustin: I am wondering if the punctual Hilbert scheme has a cell decomposition into linear pieces, I.e. cells of the form A^n. If such a decomposition exists, then I suspect one might use techniques in Gottsche's paper to show the motive of Hilbert scheme of points can be written as a polynomial of symmetric power and the Lefschetz motive L=[A^1]... I am interested to know some examples or references that may be related :)

http://mathoverflow.net/questions/61641/inverse-image-as-the-left-adjoint-to-pushforward/61647#61647 minimax 2012-07-26T01:21:47Z 2012-07-26T01:21:47Z

@Torsten: This might be easy but I somehow haven't figured out properly: on page 54 of your book, it is said that one can deduce an isomorphism between composition of pullback and pullback of compositions from $f^+(g^+\mathcal{H})=(g\circ f)^+\mathcal{H}$. So I tried: sheafifying to get $(g\circ f)^{-1}\mathcal{H}=f^{-1}(g^+\mathcal{H})$; then try to establish that the morhism $f^{-1}(g^+\mathcal{H})\to f^{-1}(g^{-1}\mathcal{H}$ is an isomorphism by showing the morphism between stalks are all isomorphisms.. But then it seems one needs to use pullback respects stalks which is eatablished later.

http://mathoverflow.net/questions/51494/why-the-name-separable-space minimax 2011-01-08T20:47:14Z 2011-01-08T20:47:14Z

Ha, that's a nice observation!