Timeline for "Nice" definition of discriminant as alluded to in an answer of Qing Liu
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Feb 10, 2018 at 16:47 | history | edited | Tom Church | CC BY-SA 3.0 |
add link to unpublished Quillen paper, thanks to D. Eriksson
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| May 10, 2010 at 9:02 | vote | accept | David Holmes | ||
| May 10, 2010 at 9:02 | comment | added | David Holmes | @Brian Conrad: Yes, sorry for being unclear. @Qing Liu:Thanks you for the reference, I will look for it... | |
| May 5, 2010 at 22:44 | comment | added | Qing Liu | This comes from computations on the Hodge bundle on the moduli space of stable curves (Mumford: "Stability of projective varieties", Enseignement Mathématiques, 1977): 1+12=1-6n+6n^2 (n=2). | |
| May 5, 2010 at 15:05 | comment | added | Matthew Morrow | I would also like to know where that 13 comes from. Very mysterious. | |
| May 5, 2010 at 14:49 | comment | added | BCnrd | @David: I didn't actually say where the 13 comes from; I just said where the 12 comes from for genus 1! I assume the 13 comes out from an argument inspired by analogy with formulas from algebraic surfaces, but the oracle status of the Deligne reference is an obstruction to saying more. I would like it if someone will explain where the 13 comes from in this general setting. | |
| May 5, 2010 at 14:20 | comment | added | David Holmes | Thanks Matthew, sadly I can't access the journal at the moment, but I can probably find it in the library. Thanks to Brian for saying where the 13 comes from. | |
| May 5, 2010 at 12:52 | comment | added | Matthew Morrow | Whoops, yes, you are right, thank you. I was imagining that $K$ was perfect (i.e. characteristic zero), so that the regularity of $X$ would imply the smoothness of the generic fibre. | |
| May 5, 2010 at 12:34 | comment | added | BCnrd | The generic fiber has to be assumed smooth in the 2nd part (so the first part can be applied there). Too bad that Deligne is an oracle here -- i.e., no published reference for the proof of the existence of the asserted general isomorphism $\Delta$. Since 13 = 1 + 12, this also nicely generalizes all of the "classical" stuff with 12's in the genus-1 case. | |
| May 5, 2010 at 11:24 | history | answered | Matthew Morrow | CC BY-SA 2.5 |