most recent 30 from http://mathoverflow.net 2013-05-18T12:54:15Z http://mathoverflow.net/feeds/user/392 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/68546/teaching-a-pedagogy-course/68581#68581 known google 2011-06-23T02:58:55Z 2011-06-23T02:58:55Z

<p>Alas, here is something unpleasant you should include: you should explain the basics of how to handle a student you suspect is cheating. Different universities have different policies/procedures. The last thing you want is to have a student get off the hook for a procedural error, or worse yet, be sued for not following procedure.</p>

http://mathoverflow.net/questions/64919/linking-to-code-in-a-paper/64985#64985 known google 2011-05-14T13:28:29Z 2011-05-14T13:28:29Z

<p>Like Poloni, I put the code in the arXiv. However, I place in the .tex sourcefile, right after ''\end{document}''. Then, on the comments section of the submission I'll write something along the lines of ''magma/sage code included at the end of sourcefile.''</p>

http://mathoverflow.net/questions/64905/which-book-would-you-like-to-see-texified/64907#64907 known google 2011-05-13T16:46:26Z 2011-05-13T16:46:26Z

<p>EGA, with hyperlinks for easy navigation.</p>

http://mathoverflow.net/questions/61515/life-after-hartshorne-the-book-not-the-person/61553#61553 known google 2011-04-13T14:58:05Z 2011-04-13T14:58:05Z

<p>Lazarsfeld's book ``Positivity in Algebraic geometry'' contains a wealth of important material and is masterfully written. Anyone doing algebraic geometry today will greatly benefit from being familiar with the contents of this book.</p> <p>Edit: here is a blog post by Burt Totaro on the importance of this topic/book:</p> <p><a href="http://burttotaro.wordpress.com/2011/01/11/why-you-should-care-about-positivity/" rel="nofollow">http://burttotaro.wordpress.com/2011/01/11/why-you-should-care-about-positivity/</a></p>

http://mathoverflow.net/questions/61055/elliptic-curves-over-global-function-fields/61064#61064 known google 2011-04-08T13:42:45Z 2011-04-08T13:42:45Z

<p>Douglas Ulmer wrote up expository notes for his short course at PArk City on precisely this topic:</p> <p><a href="http://arxiv.org/abs/1101.1939" rel="nofollow">http://arxiv.org/abs/1101.1939</a></p> <p>This might be a good place to start.</p>

http://mathoverflow.net/questions/59511/the-circle-method-and-the-binary-goldbach-problem/59575#59575 known google 2011-03-25T16:02:01Z 2011-03-25T16:02:01Z

<p>On a reference for the circle method: The book ``Analytic methods for diophantine equations and diophantine inequalities'' by Harold Davenport is superb. This is how I learned the circle method and some of its applications, and I highly recommend it.</p>

http://mathoverflow.net/questions/58926/blow-ups-at-points-in-non-general-position/58973#58973 known google 2011-03-20T14:01:01Z 2011-03-20T14:01:01Z

<p>I'll just add to Francesco's answer by saying that general position of the points on the plane is equivalent to ampleness of the anticanonical sheaf $\omega_X^{\otimes -1}$.</p> <p>The key observation is that on a del Pezzo surface, an irreducible negative curve ($C^2 &lt; 0$) must be an exceptional curve (i.e. $C^2 = C\cdot K_X = -1$). This follow from the adjunction formula and the Nakai-Moishezon criterion. </p> <p>If you blow up 3 colinear points, then the strict transform of the line containing these points will have self-intersection $-2$, which is not allowed by the key observation. Similiarly for the strict transform of a conic through 6 blown-up points. There is one more condition you have to impose: if you blow up 8 points, they cannot lie on a singular cubic with one of the points at the singularity.</p> <p>If you relax the requirement that $\omega_X^{\otimes -1}$ be ample to just big and nef, then you can have some degenerate point configurations: this time $C^2 = -2$ is allowed, so 3 colinear points ar OK. However, 4 colinear points would not be OK.</p>

http://mathoverflow.net/questions/56123/fast-turn-around-times/56126#56126 known google 2011-02-21T01:07:25Z 2011-02-21T01:07:25Z

<p>International Math Research Notices is a journal that accepts `general' papers and has a reputation for turning papers around quickly. It is in fact part of their mission statement to do so.</p>

http://mathoverflow.net/questions/55546/which-areas-of-arithmetic-algebraic-geometry-can-be-learned-as-black-boxes-and/55578#55578 known google 2011-02-16T03:20:25Z 2011-02-16T03:20:25Z

<p>I have found Groebner bases to be incredibly useful for testing concrete ideas about varieties, and although I did spend time learning how they work, all I've ever really needed to know is how to interpret the results of a Groebner Basis calculation, and how to choose monomial orders that will produce useful answers. I don't actually know how the most efficient algorithms and their implementations (Fauguère F4 and F5) arrive at an answer---the textbook algorithms are painfully slow for complicated calculations.</p>

http://mathoverflow.net/questions/42406/why-certain-diophantine-equations-are-interesting-and-others-are-not/42518#42518 known google 2010-10-17T16:42:35Z 2010-10-17T16:42:35Z

<p>My point of view is that one is really interested in the rational points of a particular variety (or class of varieties). The diophantine equation ``comes along for the ride,'' so to speak. For example, one is interested in questions like: does a variety have a rational point? Are the points dense for various topologies (Zariski, adelic)? Does the class of varieties our particular example comes from satisfy the Hasse principle?</p> <p>It turns out that the answers to these questions tend to be invariant under birational transformations: e.g. if $k$ is a number field, the Lang-Nishimura lemma says that if $X' \to X$ is a birational map between proper integral $k$-varieties then $X'$ has a smooth $k$-point if and only if $X$ has a smooth $k$-point.</p> <p>This suggests that we let birational classification results help us decide which classes of varieties (and hence what kinds of diophantine equations) to study. Morally, the more geometry we know about a particular birational class, the more we'll be able to say about the arithmetic of the variety (and hence the solutions of the associated diophantine equations), which is to say I strongly agree with JSE's last paragraph.</p>

http://mathoverflow.net/questions/55/supersingular-elliptic-curves/598#598 known google 2009-10-15T13:59:34Z 2009-10-15T13:59:34Z

<p>I'd like to add a question to this discussion: the endomorphism ring of a supersingular elliptic curve is not just an order in a quaternion algebra, it is a <em>maximal</em> order in such an algebra. Is there a simple explanation for this? </p>

http://mathoverflow.net/questions/358/examples-of-great-mathematical-writing/596#596 known google 2009-10-15T13:52:17Z 2009-10-15T13:52:17Z

<p>Lazarsfeld's book <em>Positivity in Algebraic Geometry</em> seems to fit the category ``Anyone in my field who hasn't read this paper has led an impoverished existence.'' </p> <p>I agree with Scott on `anything Serre.' His FAC and GAGA are gems; they will change your life.</p>

http://mathoverflow.net/questions/104511/a-n-whiteheads-algebra-in-process-and-reality known google 2012-08-11T20:52:43Z 2012-08-11T20:52:43Z

Please take a look at <a href="http://mathoverflow.net/faq#whatquestions" rel="nofollow">mathoverflow.net/faq#whatquestions</a> MO is simply not a venue for this type of discussion.

http://mathoverflow.net/questions/66075/the-half-life-of-a-theorem-or-arnolds-principle-at-work/66081#66081 known google 2011-05-26T23:12:21Z 2011-05-26T23:12:21Z

What boggles me most is: what did people studying metabolic curves do <i>before</i> Tai rediscovered the Trapezium rule?

http://mathoverflow.net/questions/61794/the-diophantine-eq-x4-y4-1z2 known google 2011-04-15T13:05:31Z 2011-04-15T13:05:31Z

It might not be unreasonable to look for a Brauer-Manin obstruction to the existence of integral points here.

http://mathoverflow.net/questions/55546/which-areas-of-arithmetic-algebraic-geometry-can-be-learned-as-black-boxes-and/55578#55578 known google 2011-02-16T04:11:42Z 2011-02-16T04:11:42Z

I couldn't agree more.