This question (which I did not ask) is whether the normalization of a local complete intersection domain is Gorenstein. Why was this closed as "off-topic"? Especially when this one, which asks whether the normalization of a Cohen-Macaulay domain is CM, was not. I could understand closing as "duplicate", because the counterexample to one works for the other (does that count as duplicate?), but "off-topic", really?

Maybe the specialists think it's too trivial to be a research question. Of course it's not a research question in itself, but I can quite easily imagine how one might come up with such a question incidentally (while doing research on an adjacent subject), and not have anyone around to ask, so MO would be the natural place to go to. (And it's reasonable first thought to think that normalization will tend, if not to improve, at least to preserve, singularities along the CM/Gorenstein/CI line.) At any rate, it's certainly not homework. Also, the user in question seems to ask reasonable questions in general (although their wording could often be improved and, perhaps as a result, they have not received much attention).

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    $\begingroup$ I think that this question is on topic, and have voted to reopen. $\endgroup$ Commented May 26, 2016 at 16:39
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    $\begingroup$ I think the reason this was closed is because the standards for what is an acceptable question on mathoverflow are much higher than it used to be in 2011. $\endgroup$ Commented May 26, 2016 at 19:48
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    $\begingroup$ @KarlSchwede And I think this kind of crazily high standards explains why I have a number of colleagues who tell me they don't dare ask their questions on MathOverflow. If there is a genuine desire for a walled garden of this sort (keeping away the plebs who think that Gorenstein might be preserved by normalization!), then I'm not going to argue against it, but I wonder if it's really a conscious decision by the community or just a vicious circle that nobody really wants. $\endgroup$
    – Gro-Tsen
    Commented May 26, 2016 at 21:28
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    $\begingroup$ (contd.) Also, it's a serious problem for the standards to change with time considering that old posts remain active indefinitely (and can be edited, commented upon, and answered to, and thus revived; and, I imagine, closed, but this doesn't happen). If the change in standards is desired, then there should be a way to mark old posts as "archived for historical purposes, but no longer up to present standards" or something. $\endgroup$
    – Gro-Tsen
    Commented May 26, 2016 at 21:34
  • $\begingroup$ I think it used to be that reasonable questions asked by ~2nd year graduate students learning their field were on topic I don't think that's the case any more. I think there are a lot of reasons for this. Math stackexchange obviously created a new forum where those questions were appropriate. I think also there used to be more time before questions were closed. I think frequently it was that the question was not that good, because the user didn't know the right question to ask. But sometimes the answers were still great, because the people writing them knew what the right question was. $\endgroup$ Commented May 27, 2016 at 4:41
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    $\begingroup$ @Gro-Tsen There are actually is such a way to mark duch questions, moderators can lock a question with the text "This question exists because it has historical significance, but it is not considered a good, on-topic question for this site, so please do not use it as evidence that you can ask similar questions here. This question and its answers are frozen and cannot be changed. More info: FAQ." $\endgroup$ Commented May 27, 2016 at 9:35
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    $\begingroup$ @KarlSchwede I think that the discussion at meta.mathoverflow.net/questions/2399 indicates a consensus that questions asked by ~2nd year graduate students learning their field are still on topic. $\endgroup$ Commented May 27, 2016 at 11:51
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    $\begingroup$ I would be the sort of person to ask such a question, if I came across some more sophisticated algebra in my work than what I was used to. If the question was phrased as a typical 'answer this question because it's on my assignment' then it's just a bad question. If there's context and so on, and background on what the person knows or has found by searching so far, then it's a good question at a slightly lower level than research frontier stuff. $\endgroup$
    – David Roberts Mod
    Commented May 28, 2016 at 0:25
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    $\begingroup$ @KarlSchwede what about graduate students learning things outside their field, which is what e.g. those in the UK who hope to get postdocs have to do? Not to mention those who have lectureships, but still need to learn such things? I refer people once again to the questions I asked about finite group theory or Lie groups on MO... $\endgroup$
    – Yemon Choi
    Commented May 28, 2016 at 1:04
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    $\begingroup$ I actually think we are much too restrictive on what is considered on topic. However, at least in the subfield of algebraic geometry, I feel that students who ask questions at the level of Hartshorne now subject themselves to near instant closure. This is of course amusing as most of the original questions here were questions at the level of Hartshorne. .. $\endgroup$ Commented May 29, 2016 at 3:22
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    $\begingroup$ @KarlSchwede I understand that you're playing the "devil's advocate", but Hartshorne does not define what a Gorenstein ring is and I feel that the concept is already, in itself, more advanced than most of what he discusses (although some will, of course, disagree, and "more advanced" is not a well-defined order). So even if we agree that Hartshorne (or GTM books in general) is not advanced enough for MO, (which I think should at least be qualified — as in "depending on how well the question has been researched ahead"), the particular case discussed here goes even beyond that. $\endgroup$
    – Gro-Tsen
    Commented May 29, 2016 at 19:28
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    $\begingroup$ I'm not sure "at the level of Hartshorne" is so well-defined. A basic question about the definition of schemes might warrant closure, but a basic question on the theorem of formal functions sounds already quite different $\endgroup$ Commented May 29, 2016 at 23:23
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    $\begingroup$ Personally, I don't think even a basic question on schemes would warrant closure (although they certainly are closed now). $\endgroup$ Commented May 30, 2016 at 16:36

1 Answer 1


As one of the users who casted a vote to close, I guess I should provide an answer.

What I did not like was the lack of effort displayed in the question. The question in itself could be fine: it is very legitimate, not so easy and somewhat natural in view of the hierarchy of rings in commutative algebra. However, it is also quite easy to find discussions of that and closely related topic in textbooks, through Google or-I guess-just by browsing the question MO detects as similar during the redaction of the title. These discussions should at least point in the right direction (in the sense that every other comparable statement fails, so probably that one too). The question showed no sign of these preliminary researches having been done.

In addition to that, it comes after a series of questions by this user (most of them deleted or asked by another account with the same name), which all pointed in the same direction in the sense that it was not hard for experts to reconstruct what the author had in mind from these questions. I actually answered one or two of those. But in the long run, it seems to me that MO is not the place to fish for ways to fix a proof by stabbing in the dark until someone provides the desired answer.

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    $\begingroup$ Thanks for the explanation. I agree that sometimes a series of questions from a single user can indicate a trend which isn't evident when an individual question is read in isolation $\endgroup$
    – Yemon Choi
    Commented May 31, 2016 at 20:07
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    $\begingroup$ As there are frequently questions which are not off-topic but whose exposition is poor, I think it would be good if there would be a close reason which reflects this. The text in the "close box" attached to such question could read e.g. "The exposition of this question appears to fall below the standards of the site. Please edit the question to improve its formulation and / or its layout, add any missing definitions or other information to make the question self-contained and correct any grammar- and spelling mistakes. Avoid copy/pasted or scanned text from third-party sources." $\endgroup$
    – Stefan Kohl Mod
    Commented Jun 2, 2016 at 19:25
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    $\begingroup$ The mouse-over text for the downvote on a question is "This question does not show any research effort; it is unclear or not useful". Poor research is explicitly a cause for downvoting, not closing. $\endgroup$ Commented Jun 4, 2016 at 3:50

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