Timeline for Schemes and meaning of "geometric intuition"
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 20, 2012 at 8:38 | comment | added | Emerton | Dear Tim, Joel is correct; when people talk of developing geometric intuition, they mean developing a feeling for how curves, surfaces, etc. behave, and using this to analyze situations of interest. Some typical specific topics in which it is common to begin with little intuition, but to progressively develop more, are: blowing up, intersection theory, projective embeddings via very ample line bundles, semi-stable reduction, minimal models, divisors moving in linear systems, deformation theory, normalization, and etale morphisms. (Of course I could list many more.) Regards, Matthew | |
| Jan 20, 2012 at 8:14 | comment | added | S. Carnahan♦ | I was thinking of closing this question, but perhaps people should be given a chance to make their voices heard without actually expounding on their inner thought processes. | |
| Jan 20, 2012 at 8:11 | answer | added | S. Carnahan♦ | timeline score: 2 | |
| Jan 20, 2012 at 8:11 | answer | added | S. Carnahan♦ | timeline score: 29 | |
| Jan 19, 2012 at 11:37 | comment | added | Martin Brandenburg | @Joel: This is an answer, there is no reason to post this as a comment. | |
| Jan 19, 2012 at 6:33 | comment | added | Steven Landsburg | Speaking as one who has worked at the far algebraic end of algebraic geometry (i.e. the part of algebraic geometry that is really commutative ring theory), I second Joel's unequivocal "yes". For those who work on more geometric problems, I'd expect the answer to be even more unequivocal, if "more unequivocal" were possible. | |
| Jan 19, 2012 at 1:51 | comment | added | Joël | "My question is then that is an algebraic geometer or arithmetic algebraic geometer working actually seeing nice pictures of lines, surfaces and curves in their head?" The short answer is a plain "Yes" without any mental reservation. | |
| Jan 19, 2012 at 1:49 | history | made wiki | Post Made Community Wiki by Tim | ||
| Jan 19, 2012 at 1:21 | history | edited | Tim | CC BY-SA 3.0 |
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| Jan 19, 2012 at 1:09 | history | asked | Tim | CC BY-SA 3.0 |