Timeline for What is a flop (and when are they conjectured to give derived equivalences)?
Current License: CC BY-SA 2.5
10 events
| when toggle format | what | by | license | comment | |
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| Jul 26, 2010 at 20:59 | comment | added | GS | Thanks Artie, especially for the reference to Kawamata's paper (which I had not read)! Together with Eugene's answer this helps a lot. | |
| Jul 25, 2010 at 11:03 | comment | added | user5117 | Also, if I remember rightly, according to Miles Reid's survey paper "Twenty-five years of 3-folds --- an old person's view", Atiyah's flop was already known to Zariski. He then goes on to claim that it is really already present in 19th century work on the standard Cremona transformation of P^3, and arrives at an original birthdate for the flop of 1837! | |
| Jul 25, 2010 at 10:58 | comment | added | user5117 | In higher dimensions, I would guess the best known result should be Theorem 1 from Kawamata's paper "Flops connect minimal models" <href arxiv.org/abs/0704.1013>. By that theorem, any two crepant resolutions (or even terminal crepant partial resolutions) are connected by a sequence of flops over the base (where flop here is in the standard sense of Kollar--Mori's book, or Wikipedia). | |
| Jul 25, 2010 at 1:47 | answer | added | Eugene Eisenstein | timeline score: 5 | |
| Jun 15, 2010 at 19:29 | answer | added | achatz | timeline score: 1 | |
| Jun 14, 2010 at 21:09 | comment | added | GS | Thanks; my understanding is that Bridgeland's theorem that crepant resolutions (in dim'n 3) are derived equivalent relies on the fact they are connected by a sequence of (Kollar's definition, which I think is the same as Wikipedia) flops. Is this now known in (any) higher dimension? Is it a conjecture (folklore or otherwise)? | |
| Jun 14, 2010 at 20:50 | comment | added | Aaron Bergman | For dimensions three, check out Bridgeland's arxiv.org/abs/math/0009053. | |
| Jun 14, 2010 at 14:36 | history | edited | GS | CC BY-SA 2.5 |
added 94 characters in body; edited tags
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| Jun 14, 2010 at 14:30 | comment | added | GS | Interestingly, Atiyah invented his flop in 1958, 5 years before Fosbury invented his, but for some reason nobody used the Atiyah flop in the 1960 Summer Olympics. | |
| Jun 14, 2010 at 14:25 | history | asked | GS | CC BY-SA 2.5 |