Timeline for Algebraic machinery for algebraic geometry
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Sep 19, 2021 at 10:00 | history | made wiki | Post Made Community Wiki by Stefan Kohl♦ | ||
| Apr 16, 2013 at 15:10 | comment | added | user5117 | I too agree with this heresy. (Maybe enough people have already agreed that it's no longer heresy.) There are plenty of nice problems in algebraic geometry one can work on with a really minimal amount of commutative and homological algebra. I'm not recommending that approach, but I think the idea, which one might get from looking at Hartshorne, that you have to know that depth equals dimension in Cohen-Macaulay rings (or whatever) before you start thinking about curves on del Pezzo surfaces, is not accurate, and holds people back. | |
| Apr 16, 2013 at 14:55 | comment | added | Hailong Dao | This is not heretical at all, that's what most people did (-: | |
| Apr 16, 2013 at 8:32 | comment | added | quim | I sympathise with your heresy, so +1. That said, people differ as to their need to understand about the engine. Everybody can drive safely knowing very little, but to be comfortable and happy with it is another thing. It does not seem advisable to start doing algebraic geometry without at least some familiarity with the content of Atiyah-Macdonald, and if the OP feels this is not enough for them, going for more won't hurt. Note that also Sándor's thoughtful answer suggests giving lower priority to CA as one goes deeper into AG. | |
| Apr 16, 2013 at 8:25 | comment | added | Jack Huizenga | I of course agree with your opinion here Dmitry. Once you've been working in the subject for a while you start to see why some of the nitpicky details are important, but it's certainly possible to go a long way without, say, ever just studying Hartshorne for 2 years. And at least for certain people, it's a lot more interesting to start doing geometry than to bash your head against concepts like flatness (which I'm not discrediting--it's extremely important, but at least in nice cases more intuitive than Hartshorne might have you believe) before having any idea what it might be good for. | |
| Apr 16, 2013 at 7:17 | history | answered | Dmitry Vaintrob | CC BY-SA 3.0 |