Timeline for Books/blogs/websites that have open problems in Algebraic geometry
Current License: CC BY-SA 4.0
20 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 7, 2023 at 13:20 | history | made wiki | Post Made Community Wiki by David Roberts♦ | ||
| S Jul 16, 2023 at 11:05 | history | bounty ended | CommunityBot | ||
| S Jul 16, 2023 at 11:05 | history | notice removed | CommunityBot | ||
| Jul 10, 2023 at 11:28 | answer | added | Carlo Beenakker | timeline score: 5 | |
| S Jul 8, 2023 at 9:22 | history | bounty started | Arnold | ||
| S Jul 8, 2023 at 9:22 | history | notice added | Arnold | Draw attention | |
| Jul 7, 2023 at 12:04 | comment | added | Arnold | @Libli I am grateful for your comments! They are very helpful for me. Thank you very much. | |
| Jul 7, 2023 at 9:11 | comment | added | Libli | @Arnold: as far as the derived categories and classical AG are concerned, the book by Huybrechts (Fourier-Mikai transforms) seems to be a must-have that has never been surpassed since. Though it has become outdated on the Hodge theoretic aspects of the story (and completely ignores the surprising number-theoretic implications of derived equivalences between schemes over the integers). | |
| Jul 7, 2023 at 9:02 | comment | added | Libli | @Arnold : as far as Mirror Symmetry is concerned, the book "Mirror Symmetry" in the Clay Mathematics institute collection looks interesting. However, due to the research interests of the editors, it almost solely focuses on the "counting invariants" aspects of the story. The homological, tropical and birational sides of Mirror Symmetry are completely ignored in that book. | |
| Jul 7, 2023 at 8:56 | comment | added | Libli | @Arnold : maybe the book "recent developments in Algebraic Geometry" edited by cn Cambridge may be of interest. Though the correct title of the book should be " recent developments in birational geometry". The four editirs ate birational geometers (and three of them are co-authors) which explain why the choice of subject in the book areca litle biaised. For instance, derived categories and mirror symmetry are strikingly under-represented in that book. | |
| Jul 7, 2023 at 8:47 | comment | added | Libli | @Arnold : not that I am aware of (though the question linked by Timothy Chow seems to be close to what you are looking for). The problem is that even reading a open problem in AG is not easy as it requires to understand many technicalities. Understanding why the problem is open seems even more difficult. | |
| Jul 6, 2023 at 12:27 | comment | added | Timothy Chow | Related: What are some open problems in algebraic geometry? | |
| Jul 6, 2023 at 11:10 | comment | added | Arnold | @Libli Is there some book in Algebraic Geometry like following in number theory( by Richard K Guy) : amazon.com/Unsolved-Problems-Number-Problem-Mathematics/dp/… | |
| Jul 6, 2023 at 9:20 | comment | added | Arnold | @Libli Thanks for your reply. I am sorry but I am not interested in applications. | |
| S Jul 6, 2023 at 7:46 | history | suggested | J. W. Tanner |
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| Jul 6, 2023 at 1:11 | review | Suggested edits | |||
| S Jul 6, 2023 at 7:46 | |||||
| Jul 5, 2023 at 14:42 | comment | added | Libli | If you are interested in application of algebraic geometry, I would however advice you to read any of Bernd Sturmfels paper. They are wonderfully well-written, require a modest amount of technicalities in AG and usually contain a lot of interesting open problems at the boundary between applied maths and AG. | |
| Jul 5, 2023 at 14:39 | comment | added | Libli | Algebraic Geometry has been one of the most active area in mathematics for the last 70 years and, in my opinion, it has reached such a high level of technicality that it seems very very difficult to attack research-style problem without the guidance and help of an enthusiastic professional researcher. | |
| Jul 5, 2023 at 12:13 | comment | added | Praphulla Koushik | I would go to mathematics section in arxiv.org.. click "algebraic geometry" option and see names and abstracts.. Doing this for 2/3 months should give an idea of what is happening in the area and may be a starting point for an interesting problem | |
| Jul 5, 2023 at 11:58 | history | asked | Arnold | CC BY-SA 4.0 |