MO editors' lounge

5:59 AM

Do you think that (perverse-sheaves) tag should be added to some of the posts which are tagged decomposition-theorem but not preverse-sheaves? I have asked a moderator (Todd Trimble) about this tag not too long ago. Since he suggested simply removing (decomposition-theorem), after the removal some of those questions might be missing the relevant tag. — Martin Sleziak 26 secs ago

Martin Sleziak

6:10 AM

Currently there are 24 such questions: mathoverflow.net/questions/tagged/… I'd say that most of them (if not all) do not have anything to do with sheaves.

Martin Sleziak

6:26 AM

This one at least mentions sheaves: Explicit Direct Summands in the Decomposition Theorem.

6

Q: Explicit Direct Summands in the Decomposition Theorem

Let f:X→Y be a semismall resolution of singularities. Then the pushforward of the constant sheaf on X is a semisimple perverse sheaf on Y. Under these conditions, I know how to calculate the direct summands of the pushforward f*ℚX[dim X]. My question is as follows: What more general statements a...

Martin Sleziak

6:37 AM

Hi Martin. I took a look and there are two questions on that list related to the BBD decomposition theorem and perverse sheaves: mathoverflow.net/questions/128822 and mathoverflow.net/questions/1039 . I guess those two could be retagged but I wouldn't consider it urgent (they have other accurate tags). — Dan Petersen 5 mins ago

6

Q: Divisibility of all entries in an intersection form

What are situations where one can conclude that all entries of an intersection form are divisible by a fixed integer? More precisely: $F \subset S$ is a proper connected (usually reducible) half-dimensional subvariety of a smooth variety $S$. In this situation one define the "refined intersect...

decomposition-theorem intersection-theory intersection-cohomology rt.representation-theory nilpotent-cone

6

Q: Explicit Direct Summands in the Decomposition Theorem

Let f:X→Y be a semismall resolution of singularities. Then the pushforward of the constant sheaf on X is a semisimple perverse sheaf on Y. Under these conditions, I know how to calculate the direct summands of the pushforward f*ℚX[dim X]. My question is as follows: What more general statements a...

ag.algebraic-geometry sheaf-theory decomposition-theorem

Martin Sleziak

8:10 AM

@MartinSleziak I have edited the tags in Combinatorial property of cross polytopes. As the top-level tags I have included co.combinatorics and mg.metric-geometry. Thanks in advance if somebody improves the choice of tags.

The question might be deleted in a year if it gains no upvotes. But it is probably better to fix the tags now than to wait a year whether or not it is deleted by roomba.

Martin Sleziak

10:19 AM

0

Q: Why does this figure do not appear?

I add a Picture "GaussBonnet with Jpeg format to the following question but it does not work. (Some possible obstructions to ) Limit cycles as closed geodesics(3) Can one help me to resolve this problem?

discussion support images

I will admit that I do not really understand what the OP is saying in his comments. Maybe somebody else is able to help?

BTW the two pictures look the same to me. (Although the links are different - in the current revision i.stack.imgur.com/YxQiy.jpg and i.stack.imgur.com/cxaM7.jpg ) Did I miss some difference? — Martin Sleziak 37 mins ago

@MartinSleziak I tried both with computer and my Phone. when I clique on the link "GaussBonnet" It try to enter i.stack.Imgur.com/.... but it fail. any Way thank you for your help. Yes the two picture are the same. I added the second one because the first one did not work. Now, according to your comment I realize that the problem is mine(by my phone and computer). — Ali Taghavi 29 mins ago

Martin Sleziak

3:36 PM

It seems that the problem with the post mentioned above has been solved:

Now I can see the picture in my computer. Sorry for my several comments and thanks for your help. — Ali Taghavi 3 hours ago

specific-question I will ask whether differential-calculus would be suitable for the (recently bumped) question How should one present curl and divergence in an undergraduate multivariable calculus class?

54

Q: How should one present curl and divergence in an undergraduate multivariable calculus class?

I am a TA for a multivariable calculus class this semester. I have also TA'd this course a few times in the past. Every time I teach this course, I am never quite sure how I should present curl and divergence. This course follows Stewart's book and does not use differential forms; we only deal wi...

mathematics-education dg.differential-geometry

Transcript for