Timeline for Algebraic machinery for algebraic geometry
Current License: CC BY-SA 3.0
15 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 19, 2021 at 10:00 | history | made wiki | Post Made Community Wiki by Stefan Kohl♦ | ||
| Jun 4, 2019 at 17:12 | comment | added | Sándor Kovács | @ZachTeitler: The ones with two stars.... :) | |
| Jun 4, 2019 at 12:38 | comment | added | Zach Teitler | @SándorKovács... which 2 exercises??? | |
| May 12, 2013 at 5:30 | comment | added | Sándor Kovács | I've just realized something, which may be wrong, but let me put it out here: In my mind "reading" Hartshorne means doing all but 2 of the exercises. If you think that book does not use the tools it developed, then you did not do the exercises. probably at least 2/3rds of the knowledge you can learn from that book is in the work you put in the exercises and what you learn from them. | |
| May 11, 2013 at 1:05 | comment | added | Emerton | I'm somewhat late to this conversation, but I'd just like to remark that a major goal of Hartshorne is to explain the geometry of Chapters 4 and 5 (curves and surfaces), and there are some people who would regard going into EGA as going in the wrong direction. | |
| Apr 19, 2013 at 12:47 | comment | added | Barbara | I second the idea of reading Liu - one can still learn cohomology later. I'm not sure Hartshorne's the first place to learn it either; I understood cohomology from Griffiths-Harris and Beauville's book on surfaces, which shows you cohomology at work in concrete cases. For a low in algebra, high in geometry basic introduction my favorite is still Kempf's book. It's not everywhere easy reading, though. If at all possible, don't do this alone. Having someone to bounce ideas with helps in any field, but I think is especially important in algebraic geometry. | |
| Apr 19, 2013 at 8:52 | comment | added | Filippo Alberto Edoardo | @ACL: uhm...I agree, Liu has (almost) no cohomology. But Hartshorne's presentation always left me unsatisfied. He introduces some tools, but I do not have the feeling that then he really uses them to the extent that homological algebra might allow. And I think that after the first 5 chapters in Liu one can easily go into EGA. Most probably, I am begin too subjective for MO, though... | |
| Apr 19, 2013 at 6:54 | comment | added | ACL | @Filippo: Unfortunately, not for cohomology. | |
| Apr 19, 2013 at 5:34 | comment | added | Filippo Alberto Edoardo | I do not know what Martin has in mind, but I find Liu's "Algebraic Geometry and Arithmetic Curves" much more suited than Hartshorne for almost everything... | |
| Apr 16, 2013 at 15:16 | comment | added | Sándor Kovács | @Martin, EGA is not a realistic introduction to algebraic geometry for most human beings. Which more recent textbook would you recommend. (Notice I added "or something similar" for exactly that reason). | |
| Apr 16, 2013 at 13:36 | comment | added | Martin Brandenburg | I wonder why still Hartshorne gets recommended these days. The material on the foundatations of sheaf theory and divisors is a big mess, when compared to EGA or other more recent textbooks. | |
| Apr 16, 2013 at 6:34 | comment | added | Sándor Kovács | @pranavk: I completely agree, and can't believe I forgot to mention it. In fact, that was the first book I learnt algebraic geometry from! | |
| Apr 16, 2013 at 5:58 | comment | added | Youngsu | I believe that the first edition of Rotman's "An Introduction to Homological Algebra" would be also a good source for homological algebra in addition to the book of Bruns-Herzog. | |
| Apr 16, 2013 at 3:34 | comment | added | user30379 | Fulton's "Algebraic Curves" does an excellent job of introducing commutative algebra in a geometric context, and its selection of exercises does an amazing job at conveying the rich interaction of geometry and algebra beyond what is done in the text. I recommend trying Fulton's book alongside Reid's, and then you can decide for yourself which you prefer. | |
| Apr 15, 2013 at 23:02 | history | answered | Sándor Kovács | CC BY-SA 3.0 |