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    $\begingroup$ How do I up-vote answers multiple times?!?! $\endgroup$ Commented Oct 24, 2009 at 23:02
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    $\begingroup$ By leaving a comment explaining that the answer is so great others just have to upvote it. You convinced me, by the way, to give my last daily vote :). $\endgroup$ Commented Oct 24, 2009 at 23:50
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    $\begingroup$ Anton: ok, the heuristics of "groups attached to points" is very incomplete, but... so how do you (heuristically) imagine a stack, you really think of it as a forest of objects and arrows over the category of schemes?? [*/G] ? Orbifolds? Orbifold curves? Gerbes? $\endgroup$ Commented Apr 25, 2010 at 19:14
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    $\begingroup$ @unknown: How do you (heuristically) imagine schemes? It's fine to use terminology like "fat point" so long as you keep in mind that the "fatness" of a point is not all the information there is: Spec(k[ε]/ε³) is different from Spec(k[x,y]/(x²,xy,y²)), even though they're both "fat points of order 3". Similarly, points of stacks do indeed have automorphism groups, but it is important not to think that that's all there is to it. I guess my point was that I feel like too many people take this heuristic as the definition, so they are not sufficiently mindful of its limitations. $\endgroup$ Commented Apr 25, 2010 at 22:56
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    $\begingroup$ This seems to me to be one of those heuristics which is very useful as a first approximation, but very misleading if one starts to think of it as the whole story. $\endgroup$ Commented Sep 27, 2010 at 18:21