Timeline for Mirror symmetry mod p?! ... Physics mod p?!
Current License: CC BY-SA 2.5
9 events
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| Feb 2, 2010 at 0:56 | comment | added | VA. | In the work of Candelas-de la Ossa-Green-Parkes, the mirror symmetry is between the complex deformations on one side and the deformations of the (complexified) Kahler parameter of its mirror. The first one you can replace by algebraic deformations; char-p is OK. But the second one is essentially non-algebraic and needs C. Here, I don't know what to do, sorry. Perhaps mine is not the best answer here (personally, I upvoted Ben-Zvi's answer). | |
| Feb 1, 2010 at 22:09 | vote | accept | Kevin H. Lin | ||
| Feb 1, 2010 at 22:09 | history | bounty ended | Kevin H. Lin | ||
| Feb 1, 2010 at 22:08 | comment | added | Kevin H. Lin | Yeah, I'm aware of the different "mirror symmetries", but as I say in the original question, what I'm most interested in is whether the "mirror conjecture" of Candelas et. al. is at all characteristic $p$ friendly. Do you know anything about this? | |
| Jan 31, 2010 at 23:11 | comment | added | VA. | Well, it says quite generally that the family of CY hypersurfaces (or c.i. as per Batyrev-Borisov) in the first toric variety is the mirror for that in the second one. Then you can apply this to all kinds of things. For example, degenerations of the CYs in the first family correspond to deformations of CYs in the second family. Etc. Yes, that includes the duality between the Hodge and Betti numbers. There are so many "mirror symmetries": combinatorial, homological... Some of them are more char-p friendly than others. | |
| Jan 31, 2010 at 22:58 | comment | added | Kevin H. Lin | By "Batyrev's combinatorial mirror symmetry", do you mean the Hodge diamond mirror symmetry? | |
| Jan 31, 2010 at 22:45 | history | edited | VA. | CC BY-SA 2.5 |
removed a typo: 'smooth' DM stack
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| Jan 31, 2010 at 22:35 | history | edited | VA. | CC BY-SA 2.5 |
couple of words
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| Jan 31, 2010 at 22:23 | history | answered | VA. | CC BY-SA 2.5 |