Timeline for Examples of Calabi-Yau that are birational to each other?
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
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| Jun 10, 2017 at 22:31 | comment | added | user21574 | See this presentation google.fr/… | |
| Jun 10, 2017 at 22:25 | comment | added | user21574 | Motto" Moduli space of Calabi-Yau varieties can be connected by using Symplectic surgery theory. Miles Reid’s Fantasy:“There is only one Calabi-Yau space” i.e "All CY connected through conifold transitions $S^3→S^2$ See my question mathoverflow.net/questions/262479/… | |
| Sep 20, 2012 at 7:47 | comment | added | temp | The reference is Kollár, Flops, 1990. | |
| Sep 9, 2012 at 23:21 | comment | added | user5117 | temp: that's right, Kawamata proved it for all dimensions in 2007. I guess it was known in dimension 3 much earlier, say by 1990, but I don't remember a precise reference. | |
| Sep 9, 2012 at 23:08 | comment | added | temp | Ah, a quick search shows it is proved for any dimension by Kawamata in 2007. | |
| Sep 9, 2012 at 23:04 | comment | added | temp | @Artie, Actually I need some clarification here: is "any two birational Calabi-Yaus are connected by flops" true for any dimension or just for dim = 3 ? | |
| Sep 9, 2012 at 18:41 | comment | added | user5117 | One other small comment is that your "e.g." is really more than an "e.g.": any two birational Calabi--Yaus (as long as they're smooth, or a bit more generally, have only terminal singularieties) are related by a sequence of flops. (Maybe you already knew that.) | |
| Sep 9, 2012 at 18:40 | comment | added | user5117 | Try looking at the paper "The movable fan of the Horrocks--Mumford quintic" by Michael Fryers. That gives an explicit example of a CY 3-fold with (IIRC) precisely 8 birational models. | |
| Sep 9, 2012 at 7:29 | answer | added | Sasha | timeline score: 4 | |
| Sep 9, 2012 at 6:42 | history | edited | temp | CC BY-SA 3.0 |
added 16 characters in body
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| Sep 9, 2012 at 5:53 | answer | added | Atsushi Kanazawa | timeline score: 4 | |
| Sep 9, 2012 at 4:46 | comment | added | YangMills | Presumably it means "biholomorphic". | |
| Sep 9, 2012 at 4:22 | comment | added | Igor Rivin | What does "isomorphic" mean in this context? | |
| Sep 9, 2012 at 2:07 | history | asked | temp | CC BY-SA 3.0 |