Timeline for theta divisor on a principally polarized abelian variety
Current License: CC BY-SA 2.5
19 events
| when toggle format | what | by | license | comment | |
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| Apr 5, 2010 at 5:36 | comment | added | BCnrd | @Pete: I think discussing things in person (as with your hypothetical student coming to my office) has a huge amount more value than most things on MO. I agree with Ben that it is better to write out what ppav means in the question. | |
| Apr 4, 2010 at 20:46 | comment | added | Ben Webster♦ | @Brian- You're right; I should have caught that one. I still stand by the principle that using acronyms is something would should be done with great care, and that it goes in a slightly different category than just the question of whether to define terms. | |
| Apr 4, 2010 at 16:00 | comment | added | Pete L. Clark | ...Let me ask you this: suppose a graduate student you knew who was reading about abelian varieties came to your office and asked you this question. Your answer wouldn't be "Look in any text on abelian varieties", would it? Rather, you would call attention to the specific fact that is used -- the surjectivity of the map $\varphi_L: \operatorname{Pic}(A) \rightarrow \operatorname{Pic}^0(A)$ and give them some idea of where this could be found in the text they are reading. (And you wouldn't claim that it's in Chapter 1, because that's simply false, and therefore quite unhelpful.) | |
| Apr 4, 2010 at 15:55 | comment | added | Pete L. Clark | Dear Brian, To me it is not really meaty enough for a homework question -- it is more like a check on the definitions. I also think that for every student who is taking a course on abelian varieties, there must be several more who are trying to learn this material on their own. It is currently a matter of debate -- within the MO community, and even within myself -- to what extent we should answer "straightforward" questions. This question in particular has had so many comments that I felt it deserved an actual answer... | |
| Apr 4, 2010 at 9:55 | comment | added | BCnrd | Hey Pete, the principle behind the comments of DL and AV is valid: this is a "homework"-level question for any course on abelian varieties, readily deduced from what is in any decent introductory book, even if not literally in Chapter 1. It doesn't seem a bad idea to discourage the posting of MO questions which are easily answered by what is found in introductory textbooks on a topic. Those books were written for a reason, after all. It's like the old story about teaching someone to fish... | |
| Apr 4, 2010 at 7:27 | comment | added | Pete L. Clark | @DL -- I'll bite: please exhibit a text on abelian varieties in which this result occurs in Chapter 1. | |
| Apr 4, 2010 at 7:26 | answer | added | Pete L. Clark | timeline score: 6 | |
| Apr 4, 2010 at 4:32 | comment | added | David Lehavi | -1: The question had a positive score, so I had to do my best to correct it. As Alexeev and Conrad already pointed, the answer is in chapter 1 of any text on Abelian varieties. | |
| Apr 4, 2010 at 4:20 | comment | added | Theo Johnson-Freyd | Hailong and Ben's comments mostly get at why I leave comments on especially terse questions asking for more content. But there's another reason. One of the most valuable, in my mind, services a place like MO provides is as an environment for folks to talk math publicly. It's not unlike Gowers' Polymath experiments in that regard. I'm unlikely to have anything mathematically useful to say in response to Wayne's question, but I do appreciate being able to understand the question --- watching other people ask and answer questions is a great way to learn foreign areas of mathematics. | |
| Apr 4, 2010 at 4:00 | history | edited | Wayne | CC BY-SA 2.5 |
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| Apr 4, 2010 at 0:53 | comment | added | BCnrd | Typing "ppav math" into Google pulls up lots of hits. | |
| Apr 4, 2010 at 0:16 | comment | added | Ben Webster♦ | Questions on MO are not just written for the people who might answer, they're also written for people searching on the internet. Defining an "effective divisor" isn't necessary in my opinion, though I would encourage it; its definition is easily found on Wikipedia. On the other hand, it's rude to use an acronym if you can't find out what it means by Googling. There's no math results (other than this question) for PPAV in the first 3 pages of Google hits. I've gone ahead and edited the question to expand the acronym. | |
| Apr 4, 2010 at 0:10 | history | edited | Ben Webster♦ | CC BY-SA 2.5 |
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| Apr 3, 2010 at 15:21 | comment | added | Charles Siegel | I'm going to agree with both Kevin and Hailong. For the asker to write all that out won't really make it more likely that say, Theo (who doesn't know ppav's) will answer, but it makes the asker think things through a bit, and it also establishes the common notation, as to which definitions are the ones that the asker thinks we should use. | |
| Apr 3, 2010 at 14:06 | comment | added | Hailong Dao | Writing things out have other benefits: helping people who don't know that much but interested to learn more easily, making it easier to find the relevant questions when you search. Plus more carefully written questions are more likely to get answers and also sort of morally force the responders to put in more efforts as well, etc. | |
| Apr 3, 2010 at 8:02 | comment | added | Kevin Buzzard | @Theo: I'm always a bit ambivalent about comments such as yours. I can see your point on one level, but on another level, if you don't what a ppav is then probably you're not going to be answering this question. I could take any question about functional analysis at MO and 'complain' that some of the terms are unknown to me, but even if they were explained to me I wouldn't be able to answer the question. | |
| Apr 3, 2010 at 5:43 | comment | added | Theo Johnson-Freyd | Please provide definitions, etc., for everything. Writing them out both helps you think about the definitions, and also lets those of us who do other areas of math have better access to the question. I've seen the definition of "effective divisor" before, but don't remember it off the top of my head, and "ppav" is just an acronym to me. | |
| Apr 3, 2010 at 4:25 | comment | added | VA. | Is that a homework problem? Why not read Mumford's "Abelian varieties" or, really, any book on abelian varieties? | |
| Apr 3, 2010 at 3:42 | history | asked | Wayne | CC BY-SA 2.5 |